From 7cad73c8009d93d2c9ee3aa9167b425e0064d221 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 20 Jun 2020 21:32:51 +0530
Subject: Delete Subspace_Example.py
---
.../Vector-Spaces/Subspaces/Subspace_Example.py | 82 ----------------------
1 file changed, 82 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
deleted file mode 100644
index ada173e..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
+++ /dev/null
@@ -1,82 +0,0 @@
-from manimlib.imports import *
-class Subspace_Example(Scene):
- def construct(self):
- sq = Square(side = 2, color=BLACK).shift(2*LEFT)
- sq.set_fill(color=RED,opacity=350)
- line1=Line(color=BLACK).shift(2*LEFT)
- line1.rotate(np.pi/2)
- line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)
- line2.scale(0.5)
- line3=Line(color=BLACK).shift(+1.5*LEFT)
- line3.scale(0.5)
- a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)
- a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)
- a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)
- a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)
- big_rect=Rectangle().scale(3).shift(0.5*DOWN)
- big_rect.set_fill(color=GREY,opacity=350)
- vec_space=TextMobject("$Vector Space$").scale(0.77).shift(4.5*RIGHT+3.5*UP)
- sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.77).shift(3.8*RIGHT+2*UP)
- self.play(ShowCreation(vec_space))
- self.play(ShowCreation(big_rect),ShowCreation(sub))
- self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))
- rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)
- rec.rotate(np.pi/2)
- rec.set_fill(color=BLUE,opacity=350)
- line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)
- line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)
- line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)
- b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)
- b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)
- b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)
- b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)
- self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
- self.wait(1)
- text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)
- text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)
- self.play(ShowCreation(text1),ShowCreation(text2))
- self.wait(3)
- self.play(FadeOut(text1),FadeOut(text2))
- rec.shift(3*LEFT+2.01*DOWN)
- line4.shift(3*LEFT+2*DOWN)
- line5.shift(3*LEFT+2*DOWN)
- line6.shift(3*LEFT+2*DOWN)
- b1.shift(3.1*LEFT+2.1*DOWN)
- b2.shift(3.1*LEFT+2.1*DOWN)
- b3.shift(2.9*LEFT+2*DOWN)
- b4.shift(2.9*LEFT+2.3*DOWN)
- self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
- self.wait(2)
-
- text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
- text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
- text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
- self.play(ShowCreation(text3),ShowCreation(text4))
- self.wait(3)
- rec.set_fill(color=GREY,opacity=350)
- self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))
- sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)
- sq1.set_fill(color=RED,opacity=350)
- sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)
- sq2.set_fill(color=RED,opacity=350)
- rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)
- rec1.set_fill(color=RED,opacity=350)
- rec2=Rectangle(height=1.5,width=1,color=BLACK)
- rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)
- self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))
- a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)
- b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)
- c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)
- d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)
- self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))
- self.wait(2.3)
- text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
- text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)
- text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)
- self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))
- self.wait(3)
-
-
-
-
-
--
cgit
From 48f264dcde24c776f501f6e8f16d5da6aa47ba4d Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 20 Jun 2020 21:34:58 +0530
Subject: Add files via upload
---
.../Vector-Spaces/Subspaces/Subspace_Example.py | 86 ++++++++++++++++++++++
1 file changed, 86 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
new file mode 100644
index 0000000..d87cd89
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
@@ -0,0 +1,86 @@
+from manimlib.imports import *
+class Subspace_Example(Scene):
+ def construct(self):
+ sq = Square(side = 2, color=BLACK).shift(2*LEFT)
+ sq.set_fill(color=RED,opacity=350)
+ line1=Line(color=BLACK).shift(2*LEFT)
+ line1.rotate(np.pi/2)
+ line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)
+ line2.scale(0.5)
+ line3=Line(color=BLACK).shift(+1.5*LEFT)
+ line3.scale(0.5)
+ a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)
+ a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)
+ a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)
+ a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)
+ big_rect1 = Rectangle().scale(3.3).shift(0.3*DOWN)
+ big_rect1.set_fill(color=GOLD,opacity=350)
+
+
+ big_rect2=Rectangle().scale(2.7).shift(0.5*DOWN)
+ big_rect2.set_fill(color=GREY,opacity=350)
+ vec_space=TextMobject("$Vector Space$",color=BLACK).scale(0.73).shift(4.65*RIGHT+2.6*UP)
+ sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.73).shift(3.8*RIGHT+1.7*UP)
+ self.play(ShowCreation(big_rect1),ShowCreation(vec_space))
+ self.play(ShowCreation(big_rect2),ShowCreation(sub))
+ self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))
+ rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)
+ rec.rotate(np.pi/2)
+ rec.set_fill(color=BLUE,opacity=350)
+ line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)
+ line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)
+ line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)
+ b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)
+ b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)
+ b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)
+ b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)
+ self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
+ self.wait(1)
+ text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)
+ text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)
+ self.play(ShowCreation(text1),ShowCreation(text2))
+ self.wait(3)
+ self.play(FadeOut(text1),FadeOut(text2))
+ rec.shift(3*LEFT+2.01*DOWN)
+ line4.shift(3*LEFT+2*DOWN)
+ line5.shift(3*LEFT+2*DOWN)
+ line6.shift(3*LEFT+2*DOWN)
+ b1.shift(3.1*LEFT+2.1*DOWN)
+ b2.shift(3.1*LEFT+2.1*DOWN)
+ b3.shift(2.9*LEFT+2*DOWN)
+ b4.shift(2.9*LEFT+2.3*DOWN)
+ self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
+ self.wait(2)
+
+ text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
+ text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
+ text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
+ self.play(ShowCreation(text3),ShowCreation(text4))
+ self.wait(3)
+ rec.set_fill(color=GREY,opacity=350)
+ self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))
+ sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)
+ sq1.set_fill(color=RED,opacity=350)
+ sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)
+ sq2.set_fill(color=RED,opacity=350)
+ rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)
+ rec1.set_fill(color=RED,opacity=350)
+ rec2=Rectangle(height=1.5,width=1,color=BLACK)
+ rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)
+ self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))
+ a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)
+ b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)
+ c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)
+ d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)
+ self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))
+ self.wait(2.3)
+ text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
+ text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)
+ text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)
+ self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))
+ self.wait(3)
+
+
+
+
+
--
cgit
From 2c81d2ccbcd01dec465c5f1186fa65b3516c56dd Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 20 Jun 2020 21:36:05 +0530
Subject: Add files via upload
---
.../Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4 | Bin 0 -> 608079 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4
new file mode 100644
index 0000000..46e1f3b
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4 differ
--
cgit
From adbdd989f5d27461c457ab21601e907241ca0fd8 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 20 Jun 2020 21:37:02 +0530
Subject: Delete Subspace_Example.gif
---
.../Vector-Spaces/Subspaces/gifs/Subspace_Example.gif | Bin 647405 -> 0 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
deleted file mode 100644
index 32b02be..0000000
Binary files a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif and /dev/null differ
--
cgit
From 75b6e721aecb4aea903b560f4c584f751b269155 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 20 Jun 2020 21:56:47 +0530
Subject: Add files via upload
---
...ate_Symmetry_and_Positivity_of_Inner_Product.py | 141 +++++++++++++++++
.../Inner_Product_Space_Example.py | 175 +++++++++++++++++++++
.../Inner-Product_Spaces/Inner_product.py | 28 ++++
.../Instances_of_Topological_Spaces.py | 36 +++++
.../Interpretation_of_Norm_as_Length.py | 42 +++++
.../Linearity_of_Inner_Product.py | 28 ++++
.../Inner-Product_Spaces/Vector_Projection.py | 43 +++++
7 files changed, 493 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Conjugate_Symmetry_and_Positivity_of_Inner_Product.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_product.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Instances_of_Topological_Spaces.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Interpretation_of_Norm_as_Length.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Linearity_of_Inner_Product.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Vector_Projection.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Conjugate_Symmetry_and_Positivity_of_Inner_Product.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Conjugate_Symmetry_and_Positivity_of_Inner_Product.py
new file mode 100644
index 0000000..1d84842
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Conjugate_Symmetry_and_Positivity_of_Inner_Product.py
@@ -0,0 +1,141 @@
+from manimlib.imports import *
+VECTORS = [[0, 2],
+ [1, 1],
+ [0, -2],
+ [1, -1],
+ [2, -2],
+ [2, 2],
+ [2, 2],
+ [-2, -1],
+ [3, 4]]
+class Scene1(LinearTransformationScene):
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": True,
+ "show_basis_vectors": False,
+ "basis_vector_stroke_width": 3,
+ }
+ def construct(self):
+ text1 = TextMobject(r"\text{$u$}",r"\text{ = $0 + 2i$, }",r"\text{$v$}",r"\text{ = $1 + i$}").scale(0.6).shift(3.5*UP+4*LEFT)
+ text1[0].set_color(YELLOW)
+ text1[2].set_color(RED)
+ text1.add_background_rectangle()
+ self.play(ShowCreation(text1))
+ text2 = TextMobject(r"\text{$\overline{u}$}",r"\text{ = $0 - 2i$, }",r"\text{$\overline{v}$}",r"\text{ = $1 - i$}").scale(0.6).shift(3*UP+4*LEFT)
+ text2[0].set_color(YELLOW)
+ text2[2].set_color(RED)
+ text2.add_background_rectangle()
+ self.play(ShowCreation(text2))
+ self.wait(2)
+ v1 = self.add_vector(VECTORS[0],color = YELLOW, stroke_width = 3.5)
+ u = TextMobject(r"$u$",color=YELLOW).shift(0.3*LEFT+2*UP).scale(0.6)
+ self.play(ShowCreation(u))
+ v1b = self.add_vector(VECTORS[2],color = YELLOW, stroke_width = 3.5)
+ ub = TextMobject(r"$\overline{u}$",color=YELLOW).shift(2*DOWN+0.3*LEFT).scale(0.6)
+ self.play(ShowCreation(ub))
+ self.wait(2)
+ v2 = self.add_vector(VECTORS[1],color = RED, stroke_width = 3.5)
+ v = TextMobject(r"$v$",color=RED).shift(1.2*RIGHT+1*UP).scale(0.6)
+ self.play(ShowCreation(v))
+ v2b = self.add_vector(VECTORS[3],color = RED, stroke_width = 3.5)
+ vb = TextMobject(r"$\overline{v}$",color=RED).shift(1.2*RIGHT+1*DOWN).scale(0.6)
+ self.play(ShowCreation(vb))
+ text3 = TextMobject(r"\text{$<u, v>$}",r"\text{ = }",r"\text{$\overline{u}$",r"\text{$\cdot$}",r"\text{$v$}",r"\text{ = }",r"\text{$2 - 2i$}").shift(2.5*UP+3.7*LEFT).scale(0.6)
+ text3[0].set_color(BLUE)
+ text3[2].set_color(YELLOW)
+ text3[4].set_color(RED)
+ text3.add_background_rectangle()
+ self.play(ShowCreation(text3))
+ self.wait(2)
+ text4 = TextMobject(r"\text{$<\overline{u, v}>$",r"\text{ = }",r"\text{$\overline{u}$",r"\text{$\cdot$}",r"\text{$v$}",r"\text{ = }",r"\text{$2 + 2i$}").shift(2*UP+3.7*LEFT).scale(0.6)
+ text4[0].set_color(BLUE)
+ text4[2].set_color(YELLOW)
+ text4[4].set_color(RED)
+ text4.add_background_rectangle()
+ line = Line(stroke_width = 1.5).scale(0.33).shift(2.2*UP+3.54*LEFT)
+ self.play(ShowCreation(text4),ShowCreation(line))
+ self.wait(2)
+ self.play(FadeOut(v1),FadeOut(v1b),FadeOut(v2),FadeOut(v2b),FadeOut(u),FadeOut(ub),FadeOut(v),FadeOut(vb))
+ v3 = self.add_vector(VECTORS[4],color = BLUE, stroke_width = 3.5)
+ uv = TextMobject(r"$\overline{u}\cdot v$",color=BLUE).shift(2.4*RIGHT+2.1*DOWN).scale(0.6)
+ self.play(ShowCreation(uv))
+ v3b = self.add_vector(VECTORS[5],color = BLUE, stroke_width = 3.5)
+ uvb = TextMobject(r"$\overline{\overline{u}\cdot v}$",color=BLUE).shift(2.4*RIGHT+2.1*UP).scale(0.6)
+ self.play(ShowCreation(uvb))
+ self.wait(2)
+ text5 = TextMobject(r"\text{$<v, u>$}",r"\text{ = }",r"\text{$\overline{v}$",r"\text{$\cdot$}",r"\text{$u$}",r"\text{ = }",r"\text{$2 + 2i$}").shift(1.5*UP+3.7*LEFT).scale(0.6)
+ text5[0].set_color(MAROON_B)
+ text5[2].set_color(RED)
+ text5[4].set_color(YELLOW)
+ text5.add_background_rectangle()
+ self.play(ShowCreation(text5))
+ self.wait(2)
+ v4 = self.add_vector(VECTORS[5],color = MAROON_B, stroke_width = 3.5)
+ vu = TextMobject(r"$\overline{v}\cdot u$",color=MAROON_B).shift(1.3*RIGHT+2.1*UP).scale(0.6)
+ self.play(ShowCreation(vu))
+ self.play(FadeOut(uvb))
+ self.wait(2)
+ text6 = TextMobject(r"\text{$<\overline{u, v}>$",r"\text{ = }",r"\text{$<v, u>$").scale(0.6).shift(0.8*UP+4.2*LEFT)
+ text6[0].set_color(BLUE)
+ text6[2].set_color(MAROON_B)
+ text6.add_background_rectangle()
+ self.play(ShowCreation(text6))
+ rect = Rectangle(height = 0.7,width = 3.5)
+ rect.surround(text6)
+ self.play(ShowCreation(rect))
+ self.wait(3)
+ self.play(FadeOut(line),FadeOut(text1),FadeOut(text2),FadeOut(text3),FadeOut(text4),FadeOut(text5),FadeOut(text6),FadeOut(v4),FadeOut(vu),FadeOut(v3),FadeOut(uv),FadeOut(rect),FadeOut(v3b))
+
+ text7 = TextMobject(r"\text{$u$}",r"\text{ = $(1 + i) > 0$}").scale(0.6).shift(3.5*UP+4.5*LEFT)
+ text7[0].set_color(YELLOW)
+ text7.add_background_rectangle()
+ self.play(ShowCreation(text7))
+ v5 = self.add_vector(VECTORS[1],color = YELLOW, stroke_width = 3.5)
+ u = TextMobject(r"$u$",color=YELLOW).shift(1.2*RIGHT+1*UP).scale(0.6)
+ self.play(ShowCreation(u))
+ self.wait(1.5)
+ text8 = TextMobject(r"\text{$<u, u>$}",r"\text{ = $(0 + 2i) > 0$ }").scale(0.6).shift(2.7*UP+4*LEFT)
+ text8[0].set_color(GREEN)
+ text8.add_background_rectangle()
+ rect1 = Rectangle(height = 0.55, width = 3.3)
+ rect1.surround(text8)
+ self.play(ShowCreation(text8),ShowCreation(rect1))
+ self.wait(2)
+ v6 = self.add_vector(VECTORS[0],color = GREEN, stroke_width = 3.5)
+ uu = TextMobject(r"$<u, u>$",color=GREEN).shift(0.8*LEFT+1.9*UP).scale(0.6)
+ self.play(ShowCreation(uu))
+ text9 = TextMobject(r"\text{$v$}",r"\text{ = $(-2 - i) < 0$}").scale(0.6).shift(1.5*UP+4.4*LEFT)
+ text9[0].set_color(RED)
+ text9.add_background_rectangle()
+ self.play(ShowCreation(text9))
+ self.wait(1.5)
+ v7 = self.add_vector(VECTORS[7],color = RED, stroke_width = 3.5)
+ v = TextMobject(r"$v$",color=RED).shift(2.2*LEFT+1*DOWN).scale(0.6)
+ self.play(ShowCreation(v))
+ self.wait(1.5)
+ text10 = TextMobject(r"\text{$<v, v>$}",r"\text{ = $(3 + 4i) > 0$ }").scale(0.6).shift(0.7*UP+4*LEFT)
+ text10[0].set_color(BLUE)
+ text10.add_background_rectangle()
+ rect2 = Rectangle(height=0.55,width=3.3)
+ rect2.surround(text10)
+ self.play(ShowCreation(text10),ShowCreation(rect2))
+ self.wait(2)
+ v8 = self.add_vector(VECTORS[8],color = BLUE, stroke_width = 3.5)
+ vv = TextMobject(r"$<v, v>$",color=BLUE).shift(2.1*RIGHT+3.8*UP).scale(0.6)
+ self.play(ShowCreation(vv))
+ self.wait(4)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py
new file mode 100644
index 0000000..1f98bad
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py
@@ -0,0 +1,175 @@
+from manimlib.imports import *
+from scipy import sin,cos
+class Inner_Product_Space_Example(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 6,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_labeled_nums" : list(range(6)),
+ "y_labeled_nums" : list(range(6))
+ }
+ def construct(self):
+ self.setup_axes(animate=True)
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2.3,color=RED)
+ curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2.3,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : 1.4, x_min=0,x_max=2.3,color=GREEN)
+ text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.77*DOWN+0.55*RIGHT)
+
+ text2 = TextMobject(r"$g(x)$").scale(0.5).shift(0.15*DOWN+0.55*RIGHT)
+ text3 = TextMobject(r"$h(x)$").scale(0.5).shift(1.03*DOWN+0.55*RIGHT)
+
+ self.play(ShowCreation(curve1),ShowCreation(text1))
+ self.wait(1)
+ self.play(ShowCreation(curve2),ShowCreation(text2))
+ self.wait(1)
+ self.play(ShowCreation(curve3),ShowCreation(text3))
+ self.wait(2)
+ curve4 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2.3,color=YELLOW)
+ text4 = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(0.6*UP+1*RIGHT)
+ self.wait(1.5)
+
+ self.play(ShowCreation(curve4),ShowCreation(text4),FadeOut(curve2),FadeOut(text2),FadeOut(curve1),FadeOut(text1))
+ self.wait(1.5)
+ text5 = TextMobject(r"\text{$<f(x) + g(x), h(x)>$ = ",r"\text{$\int_{a}^{b} (f(x) + g(x))h(x)$ $dx$}").scale(0.57).shift(4*RIGHT+3.5*UP)
+ text5[1].set_color(ORANGE)
+ self.play(ShowCreation(text5))
+
+ curve5 = self.get_graph(lambda x : (sin(x) + x)*1.6, x_min=0,x_max=2.3,color=ORANGE)
+ text6 = TextMobject(r"$(f(x) + g(x))\cdot h(x)$").scale(0.5).shift(2.2*UP+1.4*RIGHT)
+ area1 = self.get_area(curve5,0,2.3)
+ area1.set_color(ORANGE)
+ self.wait(1)
+ self.play(FadeOut(curve4),FadeOut(text4),FadeOut(curve3),FadeOut(text3),ShowCreation(curve5),ShowCreation(text6),ShowCreation(area1))
+ self.wait(2)
+ text7 = TextMobject(r"\text{$<f(x), h(x)>$ = ",r"\text{$\int_{a}^{b} (f(x)h(x)$ $dx$}").scale(0.57).shift(5*RIGHT+3*UP)
+ text7[1].set_color(BLUE)
+ self.play(ShowCreation(text7))
+ self.wait(1.5)
+ curve6 = self.get_graph(lambda x : (sin(x))*1.6, x_min=0,x_max=2.3,color=BLUE)
+ text8 = TextMobject(r"$f(x)\cdot h(x)$").scale(0.5).shift(1.4*DOWN+0.8*RIGHT)
+ area2 = self.get_area(curve6,0,2.3)
+ self.play(ShowCreation(curve6),ShowCreation(text8),ShowCreation(area2))
+ self.wait(1.5)
+ text9 = TextMobject(r"\text{$<g(x), h(x)>$ = ",r"\text{$\int_{a}^{b} (g(x)h(x)$ $dx$}").scale(0.57).shift(5*RIGHT+2.5*UP)
+ text9[1].set_color(MAROON_B)
+ self.play(ShowCreation(text9))
+ self.wait(1.5)
+ curve7 = self.get_graph(lambda x : x*1.6, x_min=0,x_max=2.3,color=MAROON_B)
+ text10 = TextMobject(r"$g(x)\cdot h(x)$").scale(0.5).shift(0.8*RIGHT+1*UP)
+ area3 = self.get_area(curve7,0,2.3)
+ area3.set_color(MAROON_B)
+ self.play(ShowCreation(curve7),ShowCreation(text10),ShowCreation(area3))
+ self.wait(2.6)
+ curve8 = self.get_graph(lambda x : (sin(x))*1.6 + x*1.6, x_min=0,x_max=2.3,color=RED_C)
+ area4 = self.get_area(curve8,0,2.3)
+ area4.set_color(RED_C)
+ text11 = TextMobject(r"$f(x)h(x) + g(x)h(x)$").scale(0.5).shift(2.2*UP + 1.4*RIGHT)
+ self.play(FadeOut(curve6),FadeOut(text8),FadeOut(curve7),FadeOut(text10),FadeOut(area2),FadeOut(area3),ShowCreation(curve8),ShowCreation(area4))
+ self.wait(1)
+ self.play(Transform(text6,text11))
+ self.wait(1.7)
+ text12 = TextMobject(r"$<f(x) + g(x), h(x)>$ = $<f(x), h(x)>$ + $<g(x), h(x)>$").scale(0.465).shift(0.7*UP+4*RIGHT)
+ rect1 = Rectangle(height=0.5)
+ rect1.surround(text12)
+ self.play(ShowCreation(text12),ShowCreation(rect1))
+ self.wait(3)
+ self.play(FadeOut(text6),FadeOut(text5),FadeOut(text7),FadeOut(text9),FadeOut(text12),FadeOut(rect1),FadeOut(curve8),FadeOut(area4),FadeOut(text11),FadeOut(curve5),FadeOut(area1))
+
+ curve2.set_color(ORANGE)
+ self.play(ShowCreation(curve1),ShowCreation(text1))
+ self.wait(1)
+ self.play(ShowCreation(curve2),ShowCreation(text2))
+ self.wait(2)
+ curve9 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2.3,color=GREEN)
+ text13 = TextMobject(r"$2f(x)$").scale(0.5).shift(1.1*DOWN+0.55*RIGHT)
+ self.play(Transform(curve1,curve9),Transform(text1,text13))
+ self.wait(1.5)
+
+ text14 = TextMobject(r"\text{$<2f(x), g(x)>$ = ",r"\text{$\int_{a}^{b} (2f(x))g(x)$ $dx$}").scale(0.57).shift(4*RIGHT+3.5*UP)
+ text14[1].set_color(YELLOW)
+ self.play(ShowCreation(text14))
+ self.wait(2.2)
+ curve10 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2.3,color=YELLOW)
+ text15 = TextMobject(r"$2f(x)\cdot g(x)$").scale(0.5).shift(1*RIGHT+0.97*UP)
+ area5 = self.get_area(curve10,0,2.3)
+ area5.set_color(YELLOW)
+ self.play(ShowCreation(area5),ShowCreation(curve10),ShowCreation(text15),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
+ self.wait(2)
+ text16 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{a}^{b} f(x)g(x)$ $dx$}").scale(0.57).shift(3.8*RIGHT+2.9*UP)
+ text16[1].set_color(TEAL)
+ self.play(ShowCreation(text16))
+ self.wait(1.7)
+ curve11 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2.3,color=TEAL)
+ area6 = self.get_area(curve11,0,2.3)
+ area6.set_color(TEAL)
+ text17 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.9*RIGHT+0.7*DOWN)
+ self.play(ShowCreation(curve11),ShowCreation(text17),ShowCreation(area6))
+ self.wait(2)
+
+ text18 = TextMobject(r"\text{$2 <f(x), g(x)>$ = ",r"\text{$2 \int_{a}^{b} f(x)g(x)$ $dx$}").scale(0.57).shift(4*RIGHT+2.3*UP)
+ text18[1].set_color(DARK_BLUE)
+ self.play(ShowCreation(text18))
+ self.wait(2)
+ curve12 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2.3,color=DARK_BLUE)
+ area7 = self.get_area(curve12,0,2.3)
+ area7.set_color(DARK_BLUE)
+ text19 = TextMobject(r"= $2( f(x)\cdot g(x) )$").scale(0.5).shift(2.5*RIGHT+0.97*UP)
+ self.play(ShowCreation(curve12),ShowCreation(area7),ShowCreation(text19),FadeOut(text17),FadeOut(area6),FadeOut(curve11))
+
+ self.wait(2.5)
+ text20 = TextMobject(r"$<2f(x), g(x)>$ = $2<f(x), g(x)>$").scale(0.57).shift(0.6*DOWN+4*RIGHT)
+ rect2 = Rectangle(height=0.5)
+ rect2.surround(text20)
+ self.play(ShowCreation(text20),ShowCreation(rect2))
+ self.wait(3)
+
+ self.play(FadeOut(text14),FadeOut(text15),FadeOut(text19),FadeOut(text16),FadeOut(text18),FadeOut(rect2),FadeOut(curve10),FadeOut(area5),FadeOut(curve12),FadeOut(area7),FadeOut(text20))
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2.3,color=YELLOW)
+ text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.77*DOWN+0.55*RIGHT)
+ self.play(ShowCreation(curve1),ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(curve2),ShowCreation(text2))
+ self.wait(1.7)
+ text21 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{a}^{b} f(x)g(x)$ $dx$}").scale(0.57).shift(3.5*RIGHT+3*UP)
+ text21[1].set_color(GREEN)
+ self.play(ShowCreation(text21))
+ self.wait(2)
+ curve13 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2.3,color=GREEN)
+ area8 = self.get_area(curve13,0,2.3)
+ area8.set_color(GREEN)
+ text22 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.8*RIGHT+0.7*DOWN)
+ self.play(ShowCreation(curve13),ShowCreation(area8),ShowCreation(text22),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
+ self.wait(2.2)
+ curve14 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2.3,color=RED)
+ area9 = self.get_area(curve14,0,2.3)
+ area9.set_color(RED)
+ self.play(ShowCreation(curve14),ShowCreation(area9))
+ text23 = TextMobject(r"= $\overline{f(x)\cdot g(x)}$").scale(0.5).shift(0.7*DOWN+2.1*RIGHT)
+ self.play(ShowCreation(text23))
+ self.wait(2)
+ text24 = TextMobject(r"For all the real functions").scale(0.5).shift(2*RIGHT+2*UP)
+ text25 = TextMobject(r"$<\overline{f(x), g(x)}>$ = $<f(x), g(x)>$").scale(0.5).shift(2*RIGHT+1.4*UP)
+ rect3 = Rectangle(height=0.7)
+ rect3.surround(text25)
+ self.play(ShowCreation(text24),ShowCreation(text25),ShowCreation(rect3))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_product.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_product.py
new file mode 100644
index 0000000..e1344f7
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_product.py
@@ -0,0 +1,28 @@
+from manimlib.imports import *
+import numpy as np
+class InnerProduct(Scene):
+ def construct(self):
+ big_box=Rectangle().scale(2.7)
+ box = Rectangle(height=2,width=2,color=DARK_GREY).set_fill(color=BLUE_B,opacity=350)
+ arrow1 = Arrow(color=RED).shift(1.8*LEFT+0.5*UP)
+ arrow2 = Arrow(color=RED).shift(1.8*LEFT+0.5*DOWN)
+ arrow3 = Arrow(color=GREEN).shift(1.8*RIGHT)
+ Inner = TextMobject("INNER",color=BLACK).scale(0.65).shift(0.2*UP)
+ Product = TextMobject("PRODUCT",color=BLACK).scale(0.65).shift(0.2*DOWN)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*UP)
+ v = TextMobject(r"$\vec{v}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*DOWN)
+ scalar = TextMobject("(Scalar)").scale(0.55).shift(3.3*RIGHT+0.4*DOWN)
+ u.v = TextMobject(r"$<\vec{u}, \vec{v}>$",color=YELLOW).scale(0.7).shift(3.3*RIGHT)
+ V = TextMobject("V").scale(0.7).shift(2*UP+3.8*RIGHT)
+ text = TextMobject(r"The Inner Product is an operation that takes $\vec{u}, \vec{v} \in$ V as inputs and gives a scalar as an output.").scale(0.55).shift(2*DOWN)
+ self.play(ShowCreation(big_box),ShowCreation(V))
+ self.play(ShowCreation(box))
+ self.play(ShowCreation(Product),ShowCreation(Inner))
+ self.wait(2)
+ self.play(ShowCreation(arrow1),ShowCreation(u))
+ self.play(ShowCreation(arrow2),ShowCreation(v))
+ self.wait(1.5)
+ self.play(ShowCreation(arrow3),ShowCreation(scalar),ShowCreation(u.v))
+ self.wait(1)
+ self.play(ShowCreation(text))
+ self.wait(10)
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Instances_of_Topological_Spaces.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Instances_of_Topological_Spaces.py
new file mode 100644
index 0000000..2b3cf14
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Instances_of_Topological_Spaces.py
@@ -0,0 +1,36 @@
+from manimlib.imports import *
+class InnerProduct(Scene):
+ def construct(self):
+
+ circle1 = Circle(color=DARK_GREY).scale(3.7)
+ circle1.set_fill(color=GOLD,opacity=350)
+ square1 = Square(color=DARK_GREY).scale(2.5)
+ square1.set_fill(color=DARK_BLUE,opacity=350)
+ square2=Square(color=DARK_GREY).scale(1.6).shift(0.2*DOWN)
+ square2.rotate(np.pi/4).set_fill(color=YELLOW,opacity=350)
+ square3 = Square(color=DARK_GREY).scale(1).shift(0.3*DOWN)
+ square3.set_fill(color=BLACK,opacity=350)
+ circle2 = Circle(color=DARK_GREY).scale(0.5).shift(0.45*DOWN)
+ circle2.set_fill(color=MAROON_A,opacity=350)
+ text1 = TextMobject("Topological Spaces",color=BLACK).scale(0.5).shift(3*UP)
+ text2 = TextMobject("Metric Spaces",color=BLACK).scale(0.5).shift(2.2*UP)
+ text3 = TextMobject("Normed",color=BLACK).scale(0.44).shift(1.4*UP)
+ text4 = TextMobject("Vector Spaces",color=BLACK).scale(0.44).shift(1.17*UP)
+ text5 = TextMobject("Inner Product",color=WHITE).scale(0.37).shift(0.5*UP)
+ text6 = TextMobject("Spaces",color=WHITE).scale(0.37).shift(0.27*UP)
+ text7 = TextMobject("Dot",color=BLACK).scale(0.37).shift(0.3*DOWN)
+ text8 = TextMobject("Product",color=BLACK).scale(0.32).shift(0.5*DOWN)
+
+
+
+
+ self.play(ShowCreation(circle1),ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(square1),ShowCreation(text2))
+ self.wait(1.5)
+ self.play(ShowCreation(square2),ShowCreation(text3),ShowCreation(text4))
+ self.wait(1.5)
+ self.play(ShowCreation(square3),ShowCreation(text5),ShowCreation(text6))
+ self.wait(1.5)
+ self.play(ShowCreation(circle2),ShowCreation(text7),ShowCreation(text8))
+ self.wait(4)
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Interpretation_of_Norm_as_Length.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Interpretation_of_Norm_as_Length.py
new file mode 100644
index 0000000..23c568d
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Interpretation_of_Norm_as_Length.py
@@ -0,0 +1,42 @@
+from manimlib.imports import *
+import numpy as np
+class Interpretation_of_norm_as_length(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_axis_width": 5,
+ "y_axis_height":5,
+ "graph_origin" : ORIGIN + 2*DOWN + 2*LEFT,
+ "enclude_zero_label": False
+
+ }
+ def construct(self):
+ self.setup_axes(animate=False)
+ dot = Dot().scale(0.5)
+ self.play(ShowCreation(dot))
+ origin = TextMobject(r"(0, 0)").scale(0.5).shift(2.5*LEFT+2.2*DOWN)
+ line1 = self.get_graph(lambda x : x, x_min=0,x_max=2,color=WHITE)
+ line2 = Line().rotate(np.pi/2).shift(1*DOWN)
+ text1 = TextMobject(r"$(v_1, 0)$").scale(0.5).shift(2.2*DOWN+0.2*RIGHT)
+ text2 = TextMobject(r"$(0, v_2)$").scale(0.5).shift(2.5*LEFT)
+ text3 = TextMobject(r"$(v_1, v_2)$").scale(0.5).shift(0.5*RIGHT)
+ text4 = TextMobject(r"$| v_1 |$",color=RED_B).scale(0.5).shift(1*LEFT+2.3*DOWN)
+ text5 = TextMobject(r"$| v_2 |$",color=RED_B).scale(0.5).shift(0.3*RIGHT+1*DOWN)
+ text6 = TextMobject(r"$\sqrt{{v_1}^2 + {v_2}^2}$",color=RED_B).scale(0.5).rotate(np.pi/4).shift(1.3*LEFT+1*DOWN)
+ line3 = Line(color=YELLOW).shift(1*LEFT+2*DOWN)
+ self.play(ShowCreation(line1),ShowCreation(line2),ShowCreation(text1),ShowCreation(text2),ShowCreation(text3),ShowCreation(origin))
+ self.wait(1.5)
+ self.play(ShowCreation(line3),ShowCreation(text4))
+ self.wait(1.5)
+ line2 = Line(color=YELLOW).rotate(np.pi/2).shift(1*DOWN)
+ self.play(ShowCreation(line2),ShowCreation(text5))
+ self.wait(1.5)
+ line1 = self.get_graph(lambda x : x, x_min=0,x_max=2,color=YELLOW)
+ self.play(ShowCreation(text6),ShowCreation(line1))
+ self.wait(4)
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Linearity_of_Inner_Product.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Linearity_of_Inner_Product.py
new file mode 100644
index 0000000..e1344f7
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Linearity_of_Inner_Product.py
@@ -0,0 +1,28 @@
+from manimlib.imports import *
+import numpy as np
+class InnerProduct(Scene):
+ def construct(self):
+ big_box=Rectangle().scale(2.7)
+ box = Rectangle(height=2,width=2,color=DARK_GREY).set_fill(color=BLUE_B,opacity=350)
+ arrow1 = Arrow(color=RED).shift(1.8*LEFT+0.5*UP)
+ arrow2 = Arrow(color=RED).shift(1.8*LEFT+0.5*DOWN)
+ arrow3 = Arrow(color=GREEN).shift(1.8*RIGHT)
+ Inner = TextMobject("INNER",color=BLACK).scale(0.65).shift(0.2*UP)
+ Product = TextMobject("PRODUCT",color=BLACK).scale(0.65).shift(0.2*DOWN)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*UP)
+ v = TextMobject(r"$\vec{v}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*DOWN)
+ scalar = TextMobject("(Scalar)").scale(0.55).shift(3.3*RIGHT+0.4*DOWN)
+ u.v = TextMobject(r"$<\vec{u}, \vec{v}>$",color=YELLOW).scale(0.7).shift(3.3*RIGHT)
+ V = TextMobject("V").scale(0.7).shift(2*UP+3.8*RIGHT)
+ text = TextMobject(r"The Inner Product is an operation that takes $\vec{u}, \vec{v} \in$ V as inputs and gives a scalar as an output.").scale(0.55).shift(2*DOWN)
+ self.play(ShowCreation(big_box),ShowCreation(V))
+ self.play(ShowCreation(box))
+ self.play(ShowCreation(Product),ShowCreation(Inner))
+ self.wait(2)
+ self.play(ShowCreation(arrow1),ShowCreation(u))
+ self.play(ShowCreation(arrow2),ShowCreation(v))
+ self.wait(1.5)
+ self.play(ShowCreation(arrow3),ShowCreation(scalar),ShowCreation(u.v))
+ self.wait(1)
+ self.play(ShowCreation(text))
+ self.wait(10)
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Vector_Projection.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Vector_Projection.py
new file mode 100644
index 0000000..b1724c1
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Vector_Projection.py
@@ -0,0 +1,43 @@
+from manimlib.imports import *
+VECTORS = [[3,1],
+ [1,3],
+ [1.96,0.65]]
+class Projection(LinearTransformationScene):
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": False,
+ "show_basis_vectors": False,
+ "basis_vector_stroke_width": 3,
+ }
+ def construct(self):
+ v1 = self.add_vector(VECTORS[0],color = YELLOW, stroke_width = 3.5)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.65).shift(3.2*RIGHT,1*UP)
+ self.play(ShowCreation(u))
+ self.wait(0.7)
+ v2 = self.add_vector(VECTORS[1],color = RED, stroke_width = 3.5)
+ v = TextMobject(r"$\vec{v}$",color=RED).scale(0.65).shift(1.2*RIGHT,3*UP)
+ self.play(ShowCreation(v))
+ self.wait(0.7)
+ angle = Arc(radius=0.6).scale(0.5)
+ theta = TextMobject(r"$\theta$").scale(0.65).shift(0.5*UP+0.5*RIGHT).rotate(np.pi/6)
+ self.play(ShowCreation(angle),ShowCreation(theta))
+ self.wait(1)
+ line1 = Line().scale(1.25).rotate(np.pi/(2)).shift(1.8*UP+1.47*RIGHT)
+ line1.rotate(np.pi/8)
+ self.play(ShowCreation(line1))
+ self.wait(1.3)
+ v3 = self.add_vector(VECTORS[2],color = BLUE, stroke_width = 3.5)
+ text1 = TextMobject(r"$\vec{v}$cos$\theta$",color=BLUE).scale(0.55).shift(1.25*RIGHT+0.26*UP).rotate(np.pi/9)
+ self.play(ShowCreation(text1))
+ self.wait(2)
+ text2 = TextMobject(r"\text{Projection on }",r"\text{$\vec{v}$}",r"\text{ onto }",r"\text{$\vec{u}$}",r"\text{ = }",r"\text{$ |\vec{v}|cos\theta$}").scale(0.6).shift(4*RIGHT+3*UP)
+ text2[1].set_color(RED)
+ text2[3].set_color(YELLOW)
+ text2[5].set_color(BLUE)
+ text2.add_background_rectangle()
+ self.play(ShowCreation(text2))
+ self.wait(4)
+
+
+
\ No newline at end of file
--
cgit
From cd6b1e54d2aa5b00a1268f21ef27c9a9be2580c8 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sun, 21 Jun 2020 21:12:56 +0530
Subject: Add files via upload
---
.../Vector-Spaces/Subspaces/Linear_Subspace.py | 37 ++++++++++++++++++++++
1 file changed, 37 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
new file mode 100644
index 0000000..868c28b
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
@@ -0,0 +1,37 @@
+from manimlib.imports import *
+class Subspace(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+ cube = Cube(stroke_width=5,color=WHITE).shift([1.5,1.5,1.5]).scale(1.5)
+ cube.set_fill(TEAL)
+
+ cube.set_opacity(0.4)
+ line = Line(color=MAROON,set_opacity=100).shift([1.5,1.5,1.5]).scale(1.5)
+ plane1 = Polygon([0,0,3],[3,0,3],[3,3,0],[0,3,0])
+ plane1.set_opacity(0.8)
+ plane1.set_fill(YELLOW)
+ plane1.set_color(YELLOW)
+
+
+ plane2 = Polygon([0,3,3],[3,3,3],[3,0,0],[0,0,0])
+ plane2.set_opacity(0.7)
+ plane2.set_fill(RED)
+ plane2.set_color(RED)
+
+ vgroup = VGroup(plane1,plane2,line,cube)
+ vgroup.shift([-1,-1,-1])
+
+
+ self.play(ShowCreation(cube))
+ self.play(ShowCreation(plane1))
+ self.play(ShowCreation(plane2))
+ self.play(ShowCreation(line))
+ self.wait(10)
+
+
+
+
\ No newline at end of file
--
cgit
From d673d5990567fe5fdb535469d1a29395ef42a0b0 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sun, 21 Jun 2020 22:58:03 +0530
Subject: Delete Linear_Subspace.py
---
.../Vector-Spaces/Subspaces/Linear_Subspace.py | 37 ----------------------
1 file changed, 37 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
deleted file mode 100644
index 868c28b..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
+++ /dev/null
@@ -1,37 +0,0 @@
-from manimlib.imports import *
-class Subspace(ThreeDScene):
-
-
- def construct(self):
- axes = ThreeDAxes()
- self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
- self.begin_ambient_camera_rotation(rate=0.09)
- cube = Cube(stroke_width=5,color=WHITE).shift([1.5,1.5,1.5]).scale(1.5)
- cube.set_fill(TEAL)
-
- cube.set_opacity(0.4)
- line = Line(color=MAROON,set_opacity=100).shift([1.5,1.5,1.5]).scale(1.5)
- plane1 = Polygon([0,0,3],[3,0,3],[3,3,0],[0,3,0])
- plane1.set_opacity(0.8)
- plane1.set_fill(YELLOW)
- plane1.set_color(YELLOW)
-
-
- plane2 = Polygon([0,3,3],[3,3,3],[3,0,0],[0,0,0])
- plane2.set_opacity(0.7)
- plane2.set_fill(RED)
- plane2.set_color(RED)
-
- vgroup = VGroup(plane1,plane2,line,cube)
- vgroup.shift([-1,-1,-1])
-
-
- self.play(ShowCreation(cube))
- self.play(ShowCreation(plane1))
- self.play(ShowCreation(plane2))
- self.play(ShowCreation(line))
- self.wait(10)
-
-
-
-
\ No newline at end of file
--
cgit
From 7bdd0b8d51fbc7fb700b6d8d1a4e2cfa3a750f76 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Wed, 24 Jun 2020 13:14:22 +0530
Subject: Add files via upload
---
.../Vector_Addition_and_Scalar_Multiplication.mp4 | Bin 0 -> 2830120 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.mp4
new file mode 100644
index 0000000..8acbb81
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.mp4 differ
--
cgit
From f911f3d1f22f6e3d1cb3fbf37490d9803962ddbd Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Wed, 24 Jun 2020 13:15:31 +0530
Subject: Delete Vector_Addition_and_Scalar_Multiplication.gif
---
.../Vector_Addition_and_Scalar_Multiplication.gif | Bin 4954730 -> 0 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif
deleted file mode 100644
index ed65f8a..0000000
Binary files a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/gifs/Vector_Addition_and_Scalar_Multiplication.gif and /dev/null differ
--
cgit
From 8d1887302b06ed1299a6eaff1492cab5ce4e7e59 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Wed, 24 Jun 2020 13:49:18 +0530
Subject: Add files via upload
---
...ugate_Symmetry_and_Positivity_of_Inner_Product.mp4 | Bin 0 -> 2989426 bytes
.../Inner-Product_Spaces/gifs2/InnerProduct.gif | Bin 0 -> 219685 bytes
.../gifs2/Inner_Product_Space_Example.mp4 | Bin 0 -> 3450822 bytes
.../gifs2/Instances_of_Topological_Spaces.gif | Bin 0 -> 513000 bytes
.../gifs2/Interpretation_of_norm_as_length.gif | Bin 0 -> 98767 bytes
.../gifs2/Linerity_of_Inner_Product.mp4 | Bin 0 -> 3600375 bytes
.../Inner-Product_Spaces/gifs2/Projection.gif | Bin 0 -> 1093343 bytes
7 files changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Conjugate_Symmetry_and_Positivity_of_Inner_Product.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/InnerProduct.gif
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Instances_of_Topological_Spaces.gif
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Interpretation_of_norm_as_length.gif
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Linerity_of_Inner_Product.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection.gif
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Conjugate_Symmetry_and_Positivity_of_Inner_Product.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Conjugate_Symmetry_and_Positivity_of_Inner_Product.mp4
new file mode 100644
index 0000000..6b44c55
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Conjugate_Symmetry_and_Positivity_of_Inner_Product.mp4 differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/InnerProduct.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/InnerProduct.gif
new file mode 100644
index 0000000..55b6546
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/InnerProduct.gif differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4
new file mode 100644
index 0000000..dee494f
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4 differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Instances_of_Topological_Spaces.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Instances_of_Topological_Spaces.gif
new file mode 100644
index 0000000..82d5c75
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Instances_of_Topological_Spaces.gif differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Interpretation_of_norm_as_length.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Interpretation_of_norm_as_length.gif
new file mode 100644
index 0000000..9eda7c5
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Interpretation_of_norm_as_length.gif differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Linerity_of_Inner_Product.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Linerity_of_Inner_Product.mp4
new file mode 100644
index 0000000..a1e7b29
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Linerity_of_Inner_Product.mp4 differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection.gif
new file mode 100644
index 0000000..c32fd6b
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection.gif differ
--
cgit
From 90b83827c8f46cd6705538c452a9872ebe2e7b2e Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Wed, 24 Jun 2020 14:27:13 +0530
Subject: Add files via upload
---
.../Subspaces/gifs/Basis_of_a_Subspace.mp4 | Bin 0 -> 10735096 bytes
.../Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif | Bin 0 -> 4458192 bytes
.../Subspaces/gifs/Subspace_Example.gif | Bin 0 -> 716776 bytes
3 files changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4
new file mode 100644
index 0000000..d384f80
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Basis_of_a_Subspace.mp4 differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif
new file mode 100644
index 0000000..bec7e5f
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
new file mode 100644
index 0000000..ffe71a8
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif differ
--
cgit
From 10641b7f85bb04b9e680b48881006bfadd67cbed Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Wed, 24 Jun 2020 14:44:01 +0530
Subject: Add files via upload
---
.../Function_Scalar_Multiplication.py | 62 +++++++++++++++
.../Function_Space_Addition.py | 89 ++++++++++++++++++++++
.../Integral_Properties.py | 77 +++++++++++++++++++
3 files changed, 228 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Scalar_Multiplication.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Space_Addition.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Scalar_Multiplication.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Scalar_Multiplication.py
new file mode 100644
index 0000000..ac74792
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Scalar_Multiplication.py
@@ -0,0 +1,62 @@
+from manimlib.imports import *
+from scipy import exp
+class FunctionScalarMultiplication(GraphScene):
+ CONFIG = {
+ "x_min" : -5,
+ "x_max" : 5,
+ "y_min" : -5,
+ "y_max" : 5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "graph_origin": ORIGIN,
+ }
+ def construct(self):
+ self.setup_axes(animate = True)
+ curve1 = self.get_graph(lambda x : 1/3*(x**2)+1, x_min=-2,x_max=2.5,color=ORANGE)
+ curve2 = self.get_graph(lambda x : 2*(1/3*(x**2)+1), x_min=-2,x_max=2.5,color=GOLD)
+ fx= TextMobject("$f(x)$").scale(0.6).shift(1.25*UP + 2.2*LEFT)
+ gx= TextMobject("$2 \cdot f(x)$").scale(0.6).shift(0.5*UP + 2.1*LEFT)
+ f1 = self.get_vertical_line_to_graph(-2,curve1,color=YELLOW)
+ f2 = self.get_vertical_line_to_graph(-1.5,curve1,color=YELLOW)
+ f3 = self.get_vertical_line_to_graph(-1,curve1,color=YELLOW)
+ f4 = self.get_vertical_line_to_graph(-0.5,curve1,color=YELLOW)
+ f5 = self.get_vertical_line_to_graph(0,curve1,color=YELLOW)
+ f6 = self.get_vertical_line_to_graph(0.5,curve1,color=YELLOW)
+ f7 = self.get_vertical_line_to_graph(1,curve1,color=YELLOW)
+ f8 = self.get_vertical_line_to_graph(1.5,curve1,color=YELLOW)
+ f9 = self.get_vertical_line_to_graph(2,curve1,color=YELLOW)
+ f10 = self.get_vertical_line_to_graph(2.5,curve1,color=YELLOW)
+ self.play(ShowCreation(curve1),ShowCreation(fx))
+ self.wait(1.5)
+ self.play(ShowCreation(f1),ShowCreation(f2),ShowCreation(f3),ShowCreation(f4),ShowCreation(f5),ShowCreation(f6),ShowCreation(f7),ShowCreation(f8),ShowCreation(f9),ShowCreation(f10))
+ self.wait(1.7)
+ line1=Line(color=YELLOW).shift(5*LEFT+1.8*UP).scale(0.5)
+ line1.rotate(np.pi/2)
+ scalar = TextMobject("2 x").scale(0.65).shift(5.5*LEFT+1.9*UP)
+ equal = TextMobject("=").scale(0.65).shift(4.5*LEFT+1.9*UP)
+ line2=Line(color=BLUE).shift(4*LEFT+2.3*UP)
+ line2.rotate(np.pi/2)
+ self.play(ShowCreation(line1),ShowCreation(scalar),ShowCreation(equal),ShowCreation(line2))
+ g1 = self.get_vertical_line_to_graph(-2,curve2,color=BLUE)
+ g2 = self.get_vertical_line_to_graph(-1.5,curve2,color=BLUE)
+ g3 = self.get_vertical_line_to_graph(-1,curve2,color=BLUE)
+ g4 = self.get_vertical_line_to_graph(-0.5,curve2,color=BLUE)
+ g5 = self.get_vertical_line_to_graph(0,curve2,color=BLUE)
+ g6 = self.get_vertical_line_to_graph(0.5,curve2,color=BLUE)
+ g7 = self.get_vertical_line_to_graph(1,curve2,color=BLUE)
+ g8 = self.get_vertical_line_to_graph(1.5,curve2,color=BLUE)
+ g9 = self.get_vertical_line_to_graph(2,curve2,color=BLUE)
+ g10 = self.get_vertical_line_to_graph(2.5,curve2,color=BLUE)
+ self.play(ShowCreation(g1),ShowCreation(g2),ShowCreation(g3),ShowCreation(g4),ShowCreation(g5),ShowCreation(g6),ShowCreation(g7),ShowCreation(g8),ShowCreation(g9),ShowCreation(g10))
+ self.wait(2)
+ fx2=TextMobject("2$\cdot f(x)$").scale(0.6).shift(2.6*UP+2.3*LEFT)
+ self.play(ShowCreation(curve2),ShowCreation(fx2))
+ self.wait(1.5)
+ self.play(FadeOut(curve1),FadeOut(fx))
+ sc_mult=TextMobject("$(2 f(x)) = 2f(x)$",color=GOLD).scale(0.65).shift(0.65*UP + 5*LEFT)
+ rect = Rectangle(height=0.5,width=2)
+ rect.surround(sc_mult)
+ self.play(ShowCreation(sc_mult),ShowCreation(rect))
+ self.wait(3)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Space_Addition.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Space_Addition.py
new file mode 100644
index 0000000..5ce0e11
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Function_Space_Addition.py
@@ -0,0 +1,89 @@
+from manimlib.imports import *
+from scipy import sin,exp
+class FunctionalVectorSpace(GraphScene):
+ CONFIG = {
+ "x_min" : -5,
+ "x_max" : 5,
+ "y_min" : -5,
+ "y_max" : 5,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "graph_origin": ORIGIN,
+
+
+ }
+ def construct(self):
+ self.setup_axes(animate = True)
+ curve1 = self.get_graph(lambda x : exp(x) + 0.5, x_min=-2,x_max=2.5,color=ORANGE)
+ curve2 = self.get_graph(lambda x : 1/3*(x**2)+1, x_min=-2,x_max=2.5,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : 1/3*(x**2)+1 + exp(x) + 0.5, x_min=-2,x_max=2.5,color=BLACK)
+ fx= TextMobject("$f(x)$").scale(0.6).shift(1.25*UP + 2.1*LEFT)
+ gx= TextMobject("$g(x)$").scale(0.6).shift(0.5*UP + 2.1*LEFT)
+ f1 = self.get_vertical_line_to_graph(-2,curve1,color=YELLOW)
+ f2 = self.get_vertical_line_to_graph(-1.5,curve1,color=YELLOW)
+ f3 = self.get_vertical_line_to_graph(-1,curve1,color=YELLOW)
+ f4 = self.get_vertical_line_to_graph(-0.5,curve1,color=YELLOW)
+ f5 = self.get_vertical_line_to_graph(0,curve1,color=YELLOW)
+ f6 = self.get_vertical_line_to_graph(0.5,curve1,color=YELLOW)
+ f7 = self.get_vertical_line_to_graph(1,curve1,color=YELLOW)
+ f8 = self.get_vertical_line_to_graph(1.5,curve1,color=YELLOW)
+ f9 = self.get_vertical_line_to_graph(2,curve1,color=YELLOW)
+ f10 = self.get_vertical_line_to_graph(2.5,curve1,color=YELLOW)
+
+ self.play(ShowCreation(curve1),ShowCreation(gx))
+ self.wait(1.2)
+ self.play(ShowCreation(curve2),ShowCreation(fx))
+ self.wait(1.2)
+ self.play(ShowCreation(f1),ShowCreation(f2),ShowCreation(f3),ShowCreation(f4),ShowCreation(f5),ShowCreation(f6),ShowCreation(f7),ShowCreation(f8),ShowCreation(f9),ShowCreation(f10))
+ self.wait(1.7)
+ g1 = self.get_vertical_line_to_graph(-2,curve2,color=BLUE)
+ g2 = self.get_vertical_line_to_graph(-1.5,curve2,color=BLUE)
+ g3 = self.get_vertical_line_to_graph(-1,curve2,color=BLUE)
+ g4 = self.get_vertical_line_to_graph(-0.5,curve2,color=BLUE)
+ g5 = self.get_vertical_line_to_graph(0,curve2,color=BLUE)
+ g6 = self.get_vertical_line_to_graph(0.5,curve2,color=BLUE)
+ g7 = self.get_vertical_line_to_graph(1,curve2,color=BLUE)
+ g8 = self.get_vertical_line_to_graph(1.5,curve2,color=BLUE)
+ g9 = self.get_vertical_line_to_graph(2,curve2,color=BLUE)
+ g10 = self.get_vertical_line_to_graph(2.5,curve2,color=BLUE)
+ self.play(ShowCreation(g1),ShowCreation(g2),ShowCreation(g3),ShowCreation(g4),ShowCreation(g5),ShowCreation(g6),ShowCreation(g7),ShowCreation(g8),ShowCreation(g9),ShowCreation(g10))
+ line1=Line(color=BLUE).shift(5*LEFT+2.3*UP).scale(0.25)
+ line1.rotate(np.pi/2)
+ line2=Line(color=YELLOW).shift(6*LEFT+2.5*UP).scale(0.5)
+ line2.rotate(np.pi/2)
+ line3=Line(color=PURPLE_B).shift(4*LEFT+2.7*UP).scale(0.75)
+ line3.rotate(np.pi/2)
+ add=TextMobject("+").shift(2.4*UP+5.5*LEFT).scale(0.7)
+ equal=TextMobject("=").shift(2.4*UP+4.5*LEFT).scale(0.7)
+ self.play(ShowCreation(line2),ShowCreation(line1),ShowCreation(add),ShowCreation(equal),ShowCreation(line3))
+ self.wait(2)
+ self.play(FadeOut(curve1),FadeOut(curve2))
+ self.wait(3)
+ h1 = self.get_vertical_line_to_graph(-2,curve3,color=PURPLE_B)
+ h2 = self.get_vertical_line_to_graph(-1.5,curve3,color=PURPLE_B)
+ h3 = self.get_vertical_line_to_graph(-1,curve3,color=PURPLE_B)
+ h4 = self.get_vertical_line_to_graph(-0.5,curve3,color=PURPLE_B)
+ h5 = self.get_vertical_line_to_graph(0,curve3,color=PURPLE_B)
+ h6 = self.get_vertical_line_to_graph(0.5,curve3,color=PURPLE_B)
+ h7 = self.get_vertical_line_to_graph(1,curve3,color=PURPLE_B)
+ h8 = self.get_vertical_line_to_graph(1.5,curve3,color=PURPLE_B)
+ h9 = self.get_vertical_line_to_graph(2,curve3,color=PURPLE_B)
+ h10 = self.get_vertical_line_to_graph(2.5,curve3,color=PURPLE_B)
+
+ line1.shift(1*LEFT+0.9*UP)
+ equal.shift(0.3*LEFT+0.2*UP)
+ f=TextMobject("$f(x)$").scale(0.5).shift(5.6*LEFT+3.2*UP)
+ g=TextMobject("$g(x)$").scale(0.5).shift(5.6*LEFT+2.4*UP)
+ fg=TextMobject("$(f + g)(x)$").scale(0.5).shift(2.85*UP+3.3*LEFT)
+ self.play(FadeOut(add),ShowCreation(equal),ShowCreation(line1),ShowCreation(f),ShowCreation(g),ShowCreation(fg),FadeOut(fx),FadeOut(gx))
+ self.wait(1.7)
+ self.play(ShowCreation(h1),ShowCreation(h2),ShowCreation(h3),ShowCreation(h4),ShowCreation(h5),ShowCreation(h6),ShowCreation(h7),ShowCreation(h8),ShowCreation(h9),ShowCreation(h10))
+ curve3 = self.get_graph(lambda x : 1/3*(x**2)+1 + exp(x) + 0.5, x_min=-2,x_max=2.5,color=RED_A)
+ fgx=TextMobject("$(f + g)(x)$").scale(0.5).shift(1.65*UP+2.4*LEFT)
+ self.play(ShowCreation(curve3),ShowCreation(fgx))
+ sum=TextMobject("$(f + g)(x) = f(x) + g(x)$",color=GOLD).scale(0.65).shift(0.8*UP + 5*LEFT)
+ rect = Rectangle(height=0.5,width=2)
+ rect.surround(sum)
+ self.play(ShowCreation(sum),ShowCreation(rect))
+ self.wait(3)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py
new file mode 100644
index 0000000..97c0e09
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/Integral_Properties.py
@@ -0,0 +1,77 @@
+from manimlib.imports import *
+from scipy import sin
+class Integral_Properties(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 6,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_labeled_nums" : list(range(6)),
+ "y_labeled_nums" : list(range(6))
+ }
+ def construct(self):
+ self.setup_axes(animate=False)
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2.5,color=RED)
+ curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2.5,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2.5,color=GREEN)
+ fx = TextMobject(r"$f(x)$").scale(0.5).shift(1*RIGHT+1.8*DOWN)
+ gx = TextMobject(r"$g(x)$").scale(0.5).shift(1*RIGHT)
+ sum = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(1.3*RIGHT+0.6*UP)
+ area1 = self.get_area(curve1,0,2.5)
+ area2 = self.get_area(curve2,0,2.5)
+ area3 = self.get_area(curve3,0,2.5)
+ area2.set_fill(color=PURPLE)
+ area3.set_fill(color=ORANGE)
+ text1=TextMobject(r"$\int_{0}^{2.5}$ f(x) dx = Area under the curve f(x)",color=BLUE_C).scale(0.7).shift(2.7*RIGHT+3*UP)
+ text2=TextMobject(r"$\int_{0}^{2.5}$ g(x) dx = Area under the curve g(x)",color=PURPLE_B).scale(0.7).shift(2.7*RIGHT+2.4*UP)
+ text3=TextMobject(r"Area under the curve f(x) + g(x) = $\int_{0}^{2.5} (f(x) + g(x)) dx$",color=ORANGE).scale(0.7).shift(2.7*RIGHT+1.8*UP)
+ text4=TextMobject(r"\text{$\int_{0}^{2.5}$ (f(x) + g(x)) dx}",r"\text{ = }",r"\text{ $\int_{0}^{2.5}$ f(x) dx }",r"\text{+}",r"\text{$\int_{0}^{2.5}$ g(x) dx}").scale(0.62).shift(2.7*RIGHT+2.7*UP)
+ text4[0].set_color(ORANGE)
+ text4[2].set_color(BLUE_C)
+ text4[4].set_color(PURPLE_B)
+ self.play(ShowCreation(curve1), ShowCreation(fx))
+ self.wait(1.2)
+ self.play(ShowCreation(curve2),ShowCreation(gx))
+ self.wait(1.2)
+ self.play(ShowCreation(area1))
+ self.play(ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(area2))
+ self.play(ShowCreation(text2))
+ self.wait(1.5)
+ self.play(ShowCreation(curve3),ShowCreation(sum))
+ self.play(ShowCreation(area3))
+ self.play(ShowCreation(text3))
+ self.wait(2)
+ self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3))
+ self.wait(1)
+ self.play(ShowCreation(text4))
+ self.wait(3)
+ self.play(FadeOut(curve1),FadeOut(curve2),FadeOut(area1),FadeOut(area2))
+ self.wait(1.5)
+ self.play(FadeOut(text4),FadeOut(area2),FadeOut(curve2),FadeOut(gx),FadeOut(curve3),FadeOut(sum),FadeOut(area3),ShowCreation(curve1),ShowCreation(fx))
+ self.wait(1.5)
+ self.play(ShowCreation(area1),ShowCreation(text1))
+ self.wait(1.5)
+ curve4 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2.5,color=RED)
+ area4 = self.get_area(curve4,0,2.5)
+ area4.set_fill(color=YELLOW)
+ fx2 = TextMobject(r"$2f(x)$").scale(0.7).shift(1*RIGHT+1.2*DOWN)
+ scalar_mul=TextMobject(r"$\int_{0}^{2.5} ( 2f(x) ) dx$ = 2 $\times$ Area under the curve f(x)",color=YELLOW).scale(0.7).shift(2.7*RIGHT+2.4*UP)
+ self.play(ShowCreation(curve4),ShowCreation(fx2))
+ self.wait(1)
+ self.play(ShowCreation(area4))
+ self.wait(2)
+ self.play(ShowCreation(scalar_mul))
+ self.wait(2)
+ text5=TextMobject(r"\text{$\int_{0}^{2.5}$ (2 f(x)) dx}",r"\text{ = }",r"\text{2 $\int_{0}^{2.5}$ f(x) dx }").scale(0.67).shift(2.7*RIGHT+2.7*UP)
+ text5[0].set_color(YELLOW)
+ text5[2].set_color(BLUE_C)
+ self.play(FadeOut(text1),FadeOut(scalar_mul))
+ self.wait(1)
+ self.play(ShowCreation(text5))
+ self.wait(3)
+
--
cgit
From 2051cc23cb4ecf1a66215cae77048e3e47358de5 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Wed, 24 Jun 2020 14:45:28 +0530
Subject: Add files via upload
---
.../gifs3/Addition_of_Functions.gif | Bin 0 -> 510988 bytes
.../gifs3/Function_Space_Example.gif | Bin 0 -> 1783321 bytes
.../gifs3/Scalar_Multiplicaton_of_Functions.gif | Bin 0 -> 350289 bytes
3 files changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Addition_of_Functions.gif
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Function_Space_Example.gif
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Scalar_Multiplicaton_of_Functions.gif
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Addition_of_Functions.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Addition_of_Functions.gif
new file mode 100644
index 0000000..6c42b74
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Addition_of_Functions.gif differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Function_Space_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Function_Space_Example.gif
new file mode 100644
index 0000000..996a9de
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Function_Space_Example.gif differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Scalar_Multiplicaton_of_Functions.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Scalar_Multiplicaton_of_Functions.gif
new file mode 100644
index 0000000..8fff2c8
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Function-and-Polynomial-Spaces/gifs3/Scalar_Multiplicaton_of_Functions.gif differ
--
cgit
From 2a87b8f5f12478e1894eafc8926383186a65f11c Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Wed, 24 Jun 2020 15:43:06 +0530
Subject: Add files via upload
---
.../vector-spaces/Vector-Spaces/Subspaces/Basis.py | 174 +++++++++++++++++++++
.../Vector-Spaces/Subspaces/Linear_Subspace.py | 42 +++++
2 files changed, 216 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py
new file mode 100644
index 0000000..6d2edc8
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Basis.py
@@ -0,0 +1,174 @@
+from manimlib.imports import *
+
+
+VECTORS = [[1, 2],
+ [-4, 2],
+ [-3, -3],
+ [3,-2],
+ [3,3],
+ [-2,1],
+ [-1,-3]]
+
+class Scene1(LinearTransformationScene):
+
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": False,
+ "show_basis_vectors": True,
+ "basis_vector_stroke_width": 3,
+
+ }
+ def construct(self):
+ self.setup()
+ ihat, jhat = self.get_basis_vectors()
+ labels = self.get_basis_vector_labels()
+ self.add(ihat, jhat)
+ self.add(*labels)
+
+ self.show_vector_as_basis_sum()
+ self.wait(2)
+
+ def show_vector_as_basis_sum(self):
+ text1 = TextMobject(r"Vector Space $\mathbb{R}^2$}").scale(0.8).shift(3*UP)
+ text1.add_background_rectangle()
+ self.play(ShowCreation(text1))
+ text2 = TextMobject(r"$\mathbb{R}^2$",color=BLUE_E).scale(0.8).shift(6.5*LEFT+3.5*UP)
+ text3 = TextMobject(r"\text{Basis Vectors:}",r"\text{$\hat{i}$}",r"\text{,}",r"\text{$\hat{j}$}").scale(0.7).shift(2*UP+2.5*RIGHT)
+ text3[1].set_color(GREEN_C)
+ text3[3].set_color(RED_C)
+
+ self.wait(2)
+ self.play(Transform(text1,text2))
+ self.wait(1)
+ self.play(ShowCreation(text3))
+ self.wait(1.7)
+ self.play(FadeOut(text3))
+
+ for i in range(len(VECTORS)):
+ v = self.add_vector(VECTORS[i], stroke_width = 3,color=YELLOW_D)
+
+ linei = Line(start = ORIGIN, end = VECTORS[i][0]*RIGHT)
+ linei.set_color(GREEN_C)
+ linej = Line(start = linei.get_end(),
+ end = linei.get_end() + VECTORS[i][1]*UP)
+ linej.set_color(RED_C)
+ self.play(ShowCreation(linei))
+ self.play(ShowCreation(linej))
+ vlabel = self.get_vector_label(v, str(VECTORS[i][0]) +
+ r"\imath" + "+" +
+ str(VECTORS[i][1]) +
+ r"\jmath", at_tip = True)
+ self.play(ShowCreation(vlabel))
+
+ self.play(FadeOut(linei),FadeOut(linej))
+ self.wait(1)
+ dot = Dot(v.get_end(), fill_color = v.get_stroke_color())
+ self.play(ShowCreation(dot),FadeOut(v),FadeOut(vlabel))
+ self.wait(0.3)
+
+class Scene2(LinearTransformationScene):
+ CONFIG = {
+ "num_vectors" : 16,
+ "start_color" : GREY,
+ "end_color" : YELLOW_D,
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ }
+
+ def get_vectors(self):
+ return [
+ Vector([x, y], stroke_width = 3.5)
+ for x in np.arange(-int(FRAME_X_RADIUS), int(FRAME_X_RADIUS)+0.5, 0.5)
+ for y in np.arange(-int(FRAME_Y_RADIUS), int(FRAME_Y_RADIUS)+0.5, 0.5)
+ ]
+
+ def lock_in_faded_grid(self, dimness=0.7, axes_dimness=0.5):
+ plane = self.add_plane()
+ axes = plane.get_axes()
+ plane.fade(dimness)
+ axes.set_color(WHITE)
+ axes.fade(axes_dimness)
+ self.add(axes)
+
+ def construct(self):
+ self.lock_in_faded_grid()
+
+ vectors = self.get_vectors()
+ colors = Color(self.start_color).range_to(
+ self.end_color, len(vectors)
+ )
+ for vect, color in zip(vectors, colors):
+ vect.set_color(color)
+
+ vector_group = VGroup(*vectors)
+ self.play(
+ ShowCreation(
+ vector_group,
+ run_time = 3
+ )
+ )
+
+ self.wait(1)
+
+ vectors.sort(key=lambda v: v.get_length())
+ def v_to_dot(vector):
+ return Dot(vector.get_end(), fill_color = vector.get_stroke_color())
+ self.wait()
+ rate_functions = [
+ squish_rate_func(smooth, float(x)/(len(vectors)+2), 1)
+ for x in range(len(vectors))
+ ]
+ self.play(*[
+ Transform(v, v_to_dot(v), rate_func = rf, run_time = 3)
+ for v, rf in zip(vectors, rate_functions)
+ ])
+ self.wait(2)
+ self.play_final_animation(vectors, rate_functions)
+ self.wait(2)
+
+ text1 = TextMobject(" Basis is the minimum information required to ").shift(3.1*UP).scale(0.8)
+ text2 = TextMobject("generate the whole space.").scale(0.8).shift(2.6*UP)
+
+ text1.add_background_rectangle()
+ text2.add_background_rectangle()
+
+
+
+ self.play(ShowCreation(text1),ShowCreation(text2))
+
+ self.play(ShowCreation(self.get_basis_vectors()))
+ self.wait(3)
+
+ def play_final_animation(self, vectors, rate_functions):
+
+ h_line = Line(
+ FRAME_X_RADIUS*RIGHT, FRAME_X_RADIUS*LEFT,
+ stroke_width = 0.5,
+ color = BLUE_E
+ )
+ v_line = Line(
+ FRAME_Y_RADIUS*UP, FRAME_Y_RADIUS*DOWN,
+ stroke_width = 0.5,
+ color = BLUE_E
+ )
+ line_pairs = [
+ VGroup(h_line.copy().shift(y), v_line.copy().shift(x))
+ for v in vectors
+ for x, y, z in [v.get_center()]
+ ]
+ plane = NumberPlane()
+
+ self.play(
+ ShowCreation(plane),
+ *[
+ Transform(v, p, rate_func = rf)
+ for v, p, rf in zip(vectors, line_pairs, rate_functions)
+ ]
+ )
+ self.remove(*vectors)
+
+
+
+
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
new file mode 100644
index 0000000..9062b30
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
@@ -0,0 +1,42 @@
+from manimlib.imports import *
+class Subspace(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+ cube = Cube(stroke_width=5,color=WHITE).shift([1.5,1.5,1.5]).scale(1.5)
+ cube.set_fill(TEAL)
+
+ cube.set_opacity(0.4)
+ line = Line(color=MAROON,set_opacity=100).shift([1.5,1.5,1.5]).scale(1.5)
+ plane1 = Polygon([0,0,3],[3,0,3],[3,3,0],[0,3,0])
+ plane1.set_opacity(0.8)
+ plane1.set_fill(YELLOW)
+ plane1.set_color(YELLOW)
+
+
+ plane2 = Polygon([0,3,3],[3,3,3],[3,0,0],[0,0,0])
+ plane2.set_opacity(0.7)
+ plane2.set_fill(RED)
+ plane2.set_color(RED)
+
+ vgroup = VGroup(plane1,plane2,line,cube)
+ vgroup.shift([-2,-2,-2])
+
+ text = TextMobject(r"\text{The}",r"\text{line}",r"\text{representing the intersection of the two planes is a Subspace.}",opacity = 0.6).scale(0.7).shift(3*UP)
+ text[1].set_color(MAROON)
+ self.add_fixed_in_frame_mobjects(text)
+ self.play(ShowCreation(text))
+
+
+ self.play(ShowCreation(cube))
+ self.play(ShowCreation(plane1))
+ self.play(ShowCreation(plane2))
+ self.play(ShowCreation(line))
+ self.wait(10)
+
+
+
+
\ No newline at end of file
--
cgit
From 5c947bf68465241eee3abcec931ae53054ae4eef Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 00:59:15 +0530
Subject: Add files via upload
---
.../Dual-Spaces/Basis_of_a_dual_vector_space.py | 126 +++++++++++++++++++++
.../Dual-Spaces/Dual_Basis_Example.py | 97 ++++++++++++++++
.../Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py | 38 +++++++
.../Vector-Spaces/Dual-Spaces/Duality_in_Sets.py | 25 ++++
.../Vector-Spaces/Dual-Spaces/Linear_Functional.py | 29 +++++
5 files changed, 315 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Basis_of_a_dual_vector_space.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_Basis_Example.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Duality_in_Sets.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Linear_Functional.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Basis_of_a_dual_vector_space.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Basis_of_a_dual_vector_space.py
new file mode 100644
index 0000000..630670e
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Basis_of_a_dual_vector_space.py
@@ -0,0 +1,126 @@
+from manimlib.imports import *
+class DualVectorSpace(ZoomedScene):
+
+ def construct(self):
+ c1 = Ellipse(radius = 2,color=BLUE)
+ c2 = Ellipse(radius = 2,color=YELLOW)
+ c1.rotate(np.pi/2)
+ c2.rotate(np.pi/2)
+ c1.shift(2*LEFT+0.6*UP)
+ c2.shift(2*RIGHT+0.6*UP)
+ c1.scale(2)
+ c2.scale(2)
+ self.play(ShowCreation(c1))
+ self.play(ShowCreation(c2))
+ dot1 = SmallDot(color=BLUE).shift(2*LEFT+2*UP)
+ dot2 = SmallDot(color=BLUE).shift(2*LEFT+1.5*UP)
+ dot3 = SmallDot(color=BLUE).shift(2*LEFT+1*UP)
+ dot4 = SmallDot(color=BLUE).shift(2*LEFT+0.5*UP)
+ dot5 = SmallDot(color=BLUE).shift(2*LEFT)
+ dot6 = SmallDot(color=BLUE).shift(2*LEFT+0.5*DOWN)
+ dot7 = SmallDot(color=BLUE).shift(2*LEFT+1*DOWN)
+ text1 = TextMobject(r"$V$").scale(0.6).shift(3*UP+2*LEFT)
+ text2 = TextMobject(r"$V^* = \{T:V\rightarrow F\}$").scale(0.6).shift(3*UP+2.5*RIGHT)
+ self.play(ShowCreation(dot1),ShowCreation(dot2),ShowCreation(dot3),ShowCreation(dot4),ShowCreation(dot5),ShowCreation(dot6),ShowCreation(dot7))
+ v1 = TextMobject(r"$v_1$").scale(0.5).shift(2.2*LEFT+2*UP)
+ v2 = TextMobject(r"$v_2$").scale(0.5).shift(2.2*LEFT+1.5*UP)
+ v3 = TextMobject(r"$v_3$").scale(0.5).shift(2.2*LEFT+1*UP)
+ v4 = TextMobject(r"$v_4$").scale(0.5).shift(2.2*LEFT+0.5*UP)
+ v5 = TextMobject(r"$v_5$").scale(0.5).shift(2.2*LEFT)
+ v6 = TextMobject(r"$v_6$").scale(0.5).shift(2.2*LEFT+0.5*DOWN)
+ v7 = TextMobject(r"$v_7$").scale(0.5).shift(2.2*LEFT+1*DOWN)
+ self.play(ShowCreation(v1),ShowCreation(v2),ShowCreation(v3),ShowCreation(v4),ShowCreation(v5),ShowCreation(v6),ShowCreation(v7))
+ self.play(ShowCreation(text1))
+ dot9 = SmallDot(color=YELLOW).shift(2*RIGHT+2*UP)
+ dot10 = SmallDot(color=YELLOW).shift(2*RIGHT+1.5*UP)
+ dot11 = SmallDot(color=YELLOW).shift(2*RIGHT+1*UP)
+ dot12 = SmallDot(color=YELLOW).shift(2*RIGHT+0.5*UP)
+ dot13 = SmallDot(color=YELLOW).shift(2*RIGHT)
+ dot14 = SmallDot(color=YELLOW).shift(2*RIGHT+0.5*DOWN)
+ dot15 = SmallDot(color=YELLOW).shift(2*RIGHT+1*DOWN)
+ self.play(ShowCreation(dot9),ShowCreation(dot10),ShowCreation(dot11),ShowCreation(dot12),ShowCreation(dot13),ShowCreation(dot14),ShowCreation(dot15))
+ v9 = TextMobject(r"${T_1}$").scale(0.5).shift(2.2*RIGHT+2*UP)
+ v10 = TextMobject(r"${T_2}$").scale(0.5).shift(2.2*RIGHT+1.5*UP)
+ v11 = TextMobject(r"${T_3}$").scale(0.5).shift(2.2*RIGHT+1*UP)
+ v12 = TextMobject(r"${T_4}$").scale(0.5).shift(2.2*RIGHT+0.5*UP)
+ v13 = TextMobject(r"${T_5}$").scale(0.5).shift(2.2*RIGHT)
+ v14 = TextMobject(r"${T_6}$").scale(0.5).shift(2.2*RIGHT+0.5*DOWN)
+ v15 = TextMobject(r"${T_7}$").scale(0.5).shift(2.2*RIGHT+1*DOWN)
+ self.play(ShowCreation(v9),ShowCreation(v10),ShowCreation(v11),ShowCreation(v12),ShowCreation(v13),ShowCreation(v14),ShowCreation(v15))
+ self.play(ShowCreation(text2))
+ line1 = Line(start=dot1,end=dot9,stroke_width=0.95)
+ line2 = Line(start=dot2,end=dot10,stroke_width=0.95)
+ line3 = Line(start=dot3,end=dot11,stroke_width=0.95)
+ line4 = Line(start=dot4,end=dot12,stroke_width=0.95)
+ line5 = Line(start=dot5,end=dot13,stroke_width=0.95)
+ line6 = Line(start=dot6,end=dot14,stroke_width=0.95)
+ line7 = Line(start=dot7,end=dot15,stroke_width=0.95)
+ self.play(ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(line7))
+ self.wait(1.5)
+ rect1 = Rectangle(stroke_width=0.5,width=1,height=1.9).set_fill(color=BLUE,opacity=0.3)
+ vgroup1 = VGroup(dot3,dot4,v3,v4)
+ rect1.surround(vgroup1)
+ self.play(ShowCreation(rect1))
+ text3 = TextMobject(r"Basis of $V$ = $\{v_3, v_4\}$").shift(4.6*LEFT+1*UP).scale(0.5)
+ self.play(ShowCreation(text3))
+ self.wait(1.5)
+ rect2 = Rectangle(stroke_width=0.5,width=1,height=1.7).set_fill(color=YELLOW,opacity=0.3)
+ vgroup2 = VGroup(dot11,dot12,v11,v12)
+ rect2.surround(vgroup2)
+ self.play(ShowCreation(rect2))
+ text4 = TextMobject(r"Basis of $V^*$ = $\{{T_3},{T_4} \}$").shift(4.6*RIGHT+1*UP).scale(0.5)
+ self.play(ShowCreation(text4))
+ self.wait(2.5)
+ v9.move_to(3*LEFT+3*UP).scale(1.2).set_color(YELLOW)
+ colon = TextMobject(":").shift(3*UP+2.6*LEFT)
+ vgroup3 = VGroup(line1,line2,line3,line4,line5,line6,line7)
+ vgroup4 = VGroup(v10,v11,v12,v13,v14,v15,rect1,rect2,text3,text4,c2)
+ vgroup5 = VGroup(dot9,dot10,dot11,dot12,dot13,dot14,dot15)
+ text5 = TextMobject(r"$F$").scale(0.6).shift(3*UP+2*RIGHT)
+ dot9 = SmallDot(color=GREEN).shift(2*RIGHT+2*UP)
+ dot10 = SmallDot(color=GREEN).shift(2*RIGHT+1.5*UP)
+ dot11 = SmallDot(color=GREEN).shift(2*RIGHT+1*UP)
+ dot12 = SmallDot(color=GREEN).shift(2*RIGHT+0.5*UP)
+ dot13 = SmallDot(color=GREEN).shift(2*RIGHT)
+ dot14 = SmallDot(color=GREEN).shift(2*RIGHT+0.5*DOWN)
+ dot15 = SmallDot(color=GREEN).shift(2*RIGHT+1*DOWN)
+ f1 = TextMobject(r"${f_1}$").scale(0.5).shift(2.2*RIGHT+2*UP)
+ f2 = TextMobject(r"${f_2}$").scale(0.5).shift(2.2*RIGHT+1.5*UP)
+ f3 = TextMobject(r"${f_3}$").scale(0.5).shift(2.2*RIGHT+1*UP)
+ f4 = TextMobject(r"${f_4}$").scale(0.5).shift(2.2*RIGHT+0.5*UP)
+ f5 = TextMobject(r"${f_5}$").scale(0.5).shift(2.2*RIGHT)
+ f6 = TextMobject(r"${f_6}$").scale(0.5).shift(2.2*RIGHT+0.5*DOWN)
+ f7 = TextMobject(r"${f_7}$").scale(0.5).shift(2.2*RIGHT+1*DOWN)
+ vgroup6 = VGroup(f1,f2,f3,f4,f5,f6,f7)
+ arrow = Arrow(stroke_width=1.6).scale(1.5).shift(3*UP)
+ c3 = Ellipse(radius = 2,color=GREEN)
+ c3.rotate(np.pi/2)
+ c3.shift(2*RIGHT+0.6*UP)
+ c3.scale(2)
+ self.play(ShowCreation(v9))
+ self.wait(1.5)
+ self.play(ShowCreation(arrow),ShowCreation(colon),Transform(text2,text5),FadeOut(vgroup3),FadeOut(vgroup4),FadeOut(vgroup5))
+ self.play(ShowCreation(vgroup5),ShowCreation(vgroup6),ShowCreation(c3))
+ self.wait(0.7)
+ self.play(ShowCreation(vgroup3))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_Basis_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_Basis_Example.py
new file mode 100644
index 0000000..d79ec3e
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_Basis_Example.py
@@ -0,0 +1,97 @@
+from manimlib.imports import *
+import numpy as np
+
+class Dual_Basis(GraphScene):
+ CONFIG={
+ "x_min": -7,
+ "x_max": 7,
+ "y_min": -7,
+ "y_max": 7,
+ "graph_origin": ORIGIN,
+ "x_axis_label":"$X$",
+ "y_axis_label":"$Y$",
+ "x_labeled_nums": list(np.arange(-7, 8,1)),
+ "y_labeled_nums": list(np.arange(-7, 8,1)),
+ "x_axis_width": 10,
+ "y_axis_height": 10,
+ "x_tick_frequency":1,
+ "axes_color": GREY,
+ "area_opacity": 3,
+ "num_rects": 10,
+ }
+ def construct(self):
+ self.setup_axes(animate = True)
+ XD = self.x_axis_width/(self.x_max- self.x_min)
+ YD = self.y_axis_height/(self.y_max- self.y_min)
+ a1=2*XD*RIGHT+1*YD*UP
+ a2=3*XD*RIGHT+1*YD*UP
+ vec1=Vector(direction=a1,stroke_width=2).set_color(RED_E)
+ vec1.shift(self.graph_origin)
+ v1_label=TextMobject(r"$v_1$")
+ v1_label=(v1_label.shift(self.graph_origin+a1+0.1)).scale(.6)
+ self.play(ShowCreation(vec1),ShowCreation(v1_label))
+ text1=TextMobject(r"\text{$v_1$}",r"\text{$= (2,1)$}").scale(.6)
+ text1[0].set_color(RED_E)
+ text1.shift(5*LEFT+3.5*UP)
+ self.play(ShowCreation(text1))
+ self.wait(1.5)
+ vec2=Vector(direction=a2,stroke_width=2).set_color(YELLOW_E)
+ vec2.shift(self.graph_origin)
+ v2_label=TextMobject(r"$v_2$")
+ v2_label=(v2_label.shift(self.graph_origin+a2+0.1)).scale(.6)
+ self.play(ShowCreation(vec2),ShowCreation(v2_label))
+ text2=TextMobject(r"\text{$v_2$}",r"\text{$= (3,1)$}").scale(.6)
+ text2[0].set_color(YELLOW_E)
+ text2.shift(5*LEFT+3*UP)
+ self.play(ShowCreation(text2))
+ self.wait(1.5)
+ text3=TextMobject(r"\text{${T_2}$}",r"\text{$(v_1)$}",r"\text{$= 0$}").scale(.6)
+ text3[0].set_color(BLUE)
+ text3[1].set_color(RED_E)
+ text3.shift(4.94*LEFT+2.5*UP)
+ self.play(ShowCreation(text3))
+ self.wait(1.5)
+ text4=TextMobject(r"\text{${T_2}$}",r"\text{$= x - 2y$}").scale(.6)
+ text4[0].set_color(BLUE)
+ text4.shift(4.9*LEFT+2*UP)
+ self.play(ShowCreation(text4))
+ self.wait(1.5)
+ line1 = self.get_graph(lambda x : x/2, x_min = -5,x_max=5,color=BLUE)
+ v1_dual_label = TextMobject(r"${T_2}$").scale(.6).shift(3.9*RIGHT+1.85*UP)
+ self.play(ShowCreation(line1),ShowCreation(v1_dual_label))
+ self.wait(1.5)
+ text5=TextMobject(r"\text{${T_1}$}",r"\text{$(v_2)$}",r"\text{$= 0$}").scale(.6)
+ text5[1].set_color(YELLOW_E)
+ text5[0].set_color(PINK)
+ text5.shift(4.94*LEFT+1.5*UP)
+ self.play(ShowCreation(text5))
+ self.wait(1.5)
+ line2 = self.get_graph(lambda x : x/3, x_min = -5,x_max=5,color=PINK)
+ v2_dual_label = TextMobject(r"${T_1}$").scale(.6).shift(3.9*RIGHT+1.3*UP)
+ self.play(ShowCreation(line2),ShowCreation(v2_dual_label))
+ self.wait(1.5)
+ text6=TextMobject(r"\text{${T_1}$}",r"\text{$= - x + 3y$}").scale(.6)
+ text6[0].set_color(PINK)
+ text6.shift(4.76*LEFT+1*UP)
+ self.play(ShowCreation(text6))
+ self.wait(3)
+ text7 = TextMobject(r"\text{B =}",r"\text{$[$}",r"\text{$v_1,$}",r"\text{$v_2$}",r"\text{$]$}",r"\text{=}",r"\text{$[(2,1), (3,1)]$}").scale(0.6).shift(3*UP+4.5*LEFT)
+ text7[2].set_color(RED_E)
+ text7[3].set_color(YELLOW_E)
+ self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3),FadeOut(text4),FadeOut(text5),FadeOut(text6))
+ self.play(ShowCreation(text7))
+ self.wait(0.7)
+ text8 = TextMobject(r"\text{B$^* =$}",r"\text{$[$}",r"\text{${T_1}$,}",r"\text{${T_2} $}",r"\text{$]$}",r"\text{=}",r"\text{$[-x + 3y, x - 2y]$}").scale(0.6).shift(2.3*UP+4.1*LEFT)
+ text8[3].set_color(BLUE)
+ text8[2].set_color(PINK)
+ self.play(ShowCreation(text8))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py
new file mode 100644
index 0000000..a6f501e
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Dual_of_a_Cube.py
@@ -0,0 +1,38 @@
+from manimlib.imports import *
+class Duality(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.set_camera_orientation(phi = 65*DEGREES,theta =80*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+ cube = Cube(stroke_width=5,color=WHITE).scale(2)
+ cube.set_opacity(0.2)
+ self.play(ShowCreation(cube))
+ dot1= Dot(color=RED).scale(0.85).shift([2,0,0])
+ self.play(ShowCreation(dot1))
+ dot2= Dot(color=YELLOW).scale(0.85).shift([-2,0,0])
+ self.play(ShowCreation(dot2))
+ dot3= Dot(color=BLUE).scale(0.85).shift([0,-2,0])
+ self.play(ShowCreation(dot3))
+ dot4= Dot(color=GREEN).scale(0.85).shift([0,2,0])
+ self.play(ShowCreation(dot4))
+ dot5= Dot(color=ORANGE).scale(0.85).shift([0,0,2])
+ self.play(ShowCreation(dot5))
+ dot6= Dot(color=PINK).scale(0.85).shift([0,0,-2])
+ self.play(ShowCreation(dot6))
+ line1 = Line(start=[0,0,2],end=[2,0,0],stroke_width=2.5,color=BLACK)
+ line2 = Line(start=[0,0,2],end=[-2,0,0],stroke_width=2.5,color=BLACK)
+ line3 = Line(start=[0,0,2],end=[0,-2,0],stroke_width=2.5,color=BLACK)
+ line4 = Line(start=[0,0,2],end=[0,2,0],stroke_width=2.5,color=BLACK)
+ line5 = Line(start=[2,0,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line6 = Line(start=[-2,0,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line7 = Line(start=[0,-2,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line8 = Line(start=[0,2,0],end=[0,0,-2],stroke_width=2.5,color=BLACK)
+ line9 = Line(start=[0,2,0],end=[-2,0,0],stroke_width=2.5,color=BLACK)
+ line10 = Line(start=[-2,0,0],end=[0,-2,0],stroke_width=2.5,color=BLACK)
+ line11 = Line(start=[0,-2,0],end=[2,0,0],stroke_width=2.5,color=BLACK)
+ line12 = Line(start=[2,0,0],end=[0,2,0],stroke_width=2.5,color=BLACK)
+ self.play(ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(line7),ShowCreation(line8),ShowCreation(line9),ShowCreation(line10),ShowCreation(line11),ShowCreation(line12))
+ self.wait(10)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Duality_in_Sets.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Duality_in_Sets.py
new file mode 100644
index 0000000..693017e
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Duality_in_Sets.py
@@ -0,0 +1,25 @@
+from manimlib.imports import *
+import numpy as np
+class Duality_in_sets(Scene):
+ def construct(self):
+ circle1 = Circle(radius=0.4,color=BLACK).shift(2.3*LEFT)
+ circle1.set_fill(color=RED,opacity=200)
+ rect1=Rectangle(height=2,width=2,color=GREY).shift(2*LEFT)
+ rect1.set_fill(color=DARK_BLUE,opacity=1)
+ text1 = TextMobject("S").scale(0.7).shift(0.9*UP+0.7*LEFT)
+ text2 = TextMobject("X",color=BLACK,stroke_width=0.5).scale(0.5).shift(2.3*LEFT)
+ self.play(ShowCreation(rect1),ShowCreation(text1),ShowCreation(circle1),ShowCreation(text2))
+ circle2 = Circle(radius=0.4,color=BLACK).shift(1.7*RIGHT)
+ circle2.set_fill(color=BLACK,opacity=200)
+ rect2=Rectangle(height=2,width=2,color=GREY).shift(2*RIGHT)
+ rect2.set_fill(color=DARK_BLUE,opacity=1)
+ text3 = TextMobject("S").scale(0.7).shift(0.9*UP+3.3*RIGHT)
+ text4 = TextMobject(r"X$^c$",color=BLACK,stroke_width=0.2).scale(0.5).shift(2.55*RIGHT+0.6*UP)
+ text5 = TextMobject(r"\text{The subset}",r"\text{X$^c$}",r"\text{is the dual of subset}",r"\text{X}").scale(0.6).shift(2.7*UP+0.5*LEFT)
+ text5[1].set_color(GREY)
+ text5[3].set_color(GREY)
+ self.play(ShowCreation(rect2),ShowCreation(circle2),ShowCreation(text3),ShowCreation(text4))
+ self.wait(2)
+ self.play(ShowCreation(text5))
+ self.wait(3)
+
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Linear_Functional.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Linear_Functional.py
new file mode 100644
index 0000000..6edc918
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/Linear_Functional.py
@@ -0,0 +1,29 @@
+from manimlib.imports import *
+import numpy as np
+class LinearFunctional(Scene):
+ def construct(self):
+ big_box=Rectangle().scale(2.7)
+ box = Rectangle(height=2,width=2,color=DARK_GREY).set_fill(color=PURPLE,opacity=350)
+ arrow1 = Arrow(color=RED).shift(1.8*LEFT+0.5*UP)
+ arrow2 = Arrow(color=RED).shift(1.8*LEFT+0.5*DOWN)
+ arrow3 = Arrow(color=GREEN).shift(0.5*UP+1.8*RIGHT)
+ arrow4 = Arrow(color=GREEN).shift(0.5*DOWN+1.8*RIGHT)
+ Linear = TextMobject("LINEAR",color=BLACK).scale(0.5).shift(0.2*UP)
+ Functional = TextMobject("FUNCTIONAL",color=BLACK).scale(0.5).shift(0.2*DOWN)
+ u = TextMobject(r"$\vec{u}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*UP)
+ v = TextMobject(r"$\vec{v}$",color=YELLOW).scale(0.7).shift(2.8*LEFT+0.5*DOWN)
+ f1 = TextMobject(r"$f_1$",color=YELLOW).scale(0.7).shift(2.8*RIGHT+0.5*UP)
+ f2 = TextMobject(r"$f_2$",color=YELLOW).scale(0.7).shift(2.8*RIGHT+0.5*DOWN)
+ text = TextMobject(r"The Linear Functional is a function that takes $\vec{u}, \vec{v} \in$ V as inputs and gives the output $f_1, f_2\in$ F.").scale(0.55).shift(2*DOWN)
+ self.play(ShowCreation(big_box))
+ self.play(ShowCreation(box))
+ self.play(ShowCreation(Linear),ShowCreation(Functional))
+ self.wait(2)
+ self.play(ShowCreation(arrow1),ShowCreation(u))
+ self.play(ShowCreation(arrow3),ShowCreation(f1))
+ self.wait(0.7)
+ self.play(ShowCreation(arrow2),ShowCreation(v))
+ self.play(ShowCreation(arrow4),ShowCreation(f2))
+ self.wait(1)
+ self.play(ShowCreation(text))
+ self.wait(4)
--
cgit
From 6f87e58ddc696f7a4408d83610829735885677cd Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:04:13 +0530
Subject: Add files via upload
---
.../gifs4/Basis_of_a_dual_vector_space.mp4 | Bin 0 -> 1001766 bytes
.../Dual-Spaces/gifs4/Dual_Basis_Example.mp4 | Bin 0 -> 1075193 bytes
.../Dual-Spaces/gifs4/Dual_of_a_Cube.mp4 | Bin 0 -> 1425728 bytes
.../Dual-Spaces/gifs4/Duality_in_Sets.mp4 | Bin 0 -> 126824 bytes
.../Dual-Spaces/gifs4/Linear_functional.mp4 | Bin 0 -> 261541 bytes
5 files changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Basis_of_a_dual_vector_space.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_Basis_Example.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_of_a_Cube.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Duality_in_Sets.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Linear_functional.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Basis_of_a_dual_vector_space.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Basis_of_a_dual_vector_space.mp4
new file mode 100644
index 0000000..b96f541
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diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_Basis_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_Basis_Example.mp4
new file mode 100644
index 0000000..c93be25
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diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_of_a_Cube.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Dual_of_a_Cube.mp4
new file mode 100644
index 0000000..ebfb564
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diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Duality_in_Sets.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Duality_in_Sets.mp4
new file mode 100644
index 0000000..86cc693
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diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Linear_functional.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Dual-Spaces/gifs4/Linear_functional.mp4
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index 0000000..d41fada
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--
cgit
From 5d0ee230f358aa05695af89d55f1a1c28617945b Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:23:07 +0530
Subject: Delete Vector_Addition_and_Scaling.py
---
.../Vector-Spaces/Vector_Addition_and_Scaling.py | 137 ---------------------
1 file changed, 137 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py
deleted file mode 100644
index 70af123..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scaling.py
+++ /dev/null
@@ -1,137 +0,0 @@
-from manimlib.imports import *
-import numpy as np
-
-class vectorspace(GraphScene):
- CONFIG={
- "x_min": -7,
- "x_max": 7,
- "y_min": -7,
- "y_max": 7,
- "graph_origin": ORIGIN,
- "x_axis_label":"$X$",
- "y_axis_label":"$Y$",
- "x_labeled_nums": list(np.arange(-7, 8,1)),
- "y_labeled_nums": list(np.arange(-7, 8,1)),
- "x_axis_width": 8,
- "y_axis_height": 7,
- "x_tick_frequency":1,
- "axes_color": GREY,
- "area_opacity": 3,
- "num_rects": 10,
- }
- def construct(self):
- XD = self.x_axis_width/(self.x_max- self.x_min)
- YD = self.y_axis_height/(self.y_max- self.y_min)
- a1=1*XD*RIGHT+2*YD*UP
- a2=1*XD*RIGHT+1*YD*UP
- vec1=Vector(direction=a1).set_color(RED_E)
- vec1.shift(self.graph_origin)
- vec2=Vector(direction=a2).set_color(YELLOW_E)
- vec2.shift(self.graph_origin)
- vec1_text=TextMobject(r"$\vec{a}$")
- vec2_text=TextMobject(r"$\vec{b}$")
- vec1_text=(vec1_text.shift(self.graph_origin+a1+0.2)).scale(.7)
- vec2_text=(vec2_text.shift(self.graph_origin+a2+0.2)).scale(.7)
- self.setup_axes(animate=True)
- self.wait(2)
- self.play(ShowCreation(vec1))
- self.play(ShowCreation(vec1_text))
- self.wait(.7)
- self.play(ShowCreation(vec2))
- self.play(ShowCreation(vec2_text))
- self.wait(.7)
- a=TextMobject(r"$\vec{a} = (1,2)$",color=RED_B).scale(.6)
- a.shift(3*LEFT+2.7*UP)
- b=TextMobject(r"$\vec{b} = (1,1)$",color=YELLOW_E).scale(.6)
- b.shift(3*LEFT+2*UP)
- self.play(ShowCreation(a))
- self.play(ShowCreation(b))
- self.wait(.5)
- c=TextMobject(r"$2\cdot\vec{a} = 2\cdot(1,2) = (2,4)$",color=RED_B)
- c.shift(3*LEFT+2.7*UP)
- c.scale(.6)
- self.play(Transform(a,c))
- scaling1=TextMobject(r"Scaling vector $\vec{a}$ by 2 units",color=GOLD).scale(.5)
- scaling1.shift(3.4*RIGHT+2.4*UP)
- self.play(ShowCreation(scaling1))
- a1=2*XD*RIGHT+4*YD*UP
- self.play(FadeOut(vec1_text))
- vec1_scaled=Vector(direction=a1).set_color(RED_E)
- vec1_scaled.shift(self.graph_origin)
- self.play(ShowCreation(vec1_scaled))
- self.play(FadeOut(vec1))
- vec1_scaled_text=TextMobject(r"$2\vec{a}$").scale(.7)
- vec1_scaled_text.shift(self.graph_origin+a1+0.2)
- self.play(ShowCreation(vec1_scaled_text))
- self.play(FadeOut(scaling1))
- d=TextMobject(r"$3\cdot\vec{b} = 3\cdot(1,1) = (3,3)$",color=YELLOW_E).scale(.6)
- d.shift(3*LEFT+2*UP)
- self.play(Transform(b,d))
- scaling2=TextMobject(r"Scaling vector $\vec{b}$ by 3 units",color=GOLD).scale(.5)
- scaling2.shift(3.4*RIGHT+2.4*UP)
- self.play(ShowCreation(scaling2))
- a2=3*XD*RIGHT+3*YD*UP
- self.play(FadeOut(vec2_text))
- vec2_2=Vector
- vec2_scaled=Vector(direction=a2).set_color(YELLOW_E)
- vec2_scaled.shift(self.graph_origin)
- self.play(ShowCreation(vec2_scaled))
- self.play(FadeOut(vec2))
- vec2_scaled_text=TextMobject(r"$3\vec{b}$").scale(.7)
- vec2_scaled_text.shift(self.graph_origin+a2+0.2)
- self.play(ShowCreation(vec2_scaled_text))
- self.wait(.7)
- self.play(FadeOut(scaling2))
- add = TextMobject("+").scale(.7)
- add.shift(4.8*LEFT+2*UP)
- self.play(ShowCreation(add))
- self.wait(.5)
- line = Line()
- line.shift(3*LEFT+1.6*UP)
- line.scale(1.8)
- self.play(ShowCreation(line))
- self.wait(1)
- e = TextMobject(r"$\vec{c} = 2\cdot\vec{a} + 3\cdot\vec{b} = (5,7)$",color=GREEN_D).scale(.6)
- e.shift(3*LEFT+1.3*UP)
- self.play(ShowCreation(e))
- self.wait(.5)
- add1=TextMobject("Addition of the scaled vectors",color=GOLD).scale(.5)
- add1.shift(4.1*RIGHT+2.4*UP)
- self.play(ShowCreation(add1))
- self.wait(.5)
- self.play(FadeOut(vec1_scaled_text))
- self.play(FadeOut(vec2_scaled_text))
- self.play(FadeOut(vec1_scaled))
- vec1_scaled2=Vector(direction=a1).set_color(RED_E)
- vec1_scaled2.shift(self.graph_origin+3*RIGHT*XD+3*UP*YD)
- self.play(ShowCreation(vec1_scaled2))
- a3=5*XD*RIGHT+7*YD*UP
- vec3=Vector(direction=a3).set_color(GREEN_C)
- vec3.shift(self.graph_origin)
- vec3_text=TextMobject(r"$\vec{c}$").scale(.7)
- vec3_text.shift(self.graph_origin+a3+0.2)
- self.play(ShowCreation(vec3))
- self.wait(.5)
- self.play(ShowCreation(vec3_text))
- self.wait(1)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
cgit
From 35157fabe0495dc8320cc4693cbc85db4a256871 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:24:46 +0530
Subject: Add files via upload
---
.../Vector_Addition_and_Scalar_Multiplication.py | 177 +++++++++++++++++++++
1 file changed, 177 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scalar_Multiplication.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scalar_Multiplication.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scalar_Multiplication.py
new file mode 100644
index 0000000..12c9bce
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Vector-Spaces/Vector_Addition_and_Scalar_Multiplication.py
@@ -0,0 +1,177 @@
+from manimlib.imports import *
+VECTORS = [[1, 2],
+ [1, 1],
+ [2, 2],
+ [3, 4]]
+class Scene1(LinearTransformationScene):
+ CONFIG = {
+ "include_background_plane": True,
+ "include_foreground_plane": False,
+ "show_coordinates": True,
+ "show_basis_vectors": False,
+ "basis_vector_stroke_width": 3,
+ }
+ def construct(self):
+ self.write_stuff()
+ v1 = self.add_vector(VECTORS[0],color = YELLOW, stroke_width = 3.5)
+ line1 = Line(start = ORIGIN, end = VECTORS[0][0]*RIGHT)
+ line1.set_color(RED_B)
+ line2 = Line(start = line1.get_end(), end = line1.get_end() + VECTORS[0][1]*UP)
+ line2.set_color(GREEN_D)
+ self.play(ShowCreation(line1))
+ self.play(ShowCreation(line2))
+ self.wait(0.5)
+ text1 = TextMobject("(1, 2)",color=YELLOW).scale(0.6).shift(2*UP + 1.5*RIGHT)
+ self.play(ShowCreation(text1))
+ text2 = TextMobject(r"$\vec{a}$",color = YELLOW).scale(0.8).shift(2*UP + 1.2*RIGHT)
+ text3 = TextMobject(r"\text{$\vec{a}$}",r"\text{=}",r"\text{(1, 2)}").scale(0.7).shift(5.1*LEFT + 2.5*UP)
+ text3[0].set_color(YELLOW)
+ text3[2].set_color(YELLOW)
+ self.wait(1)
+ self.play(Transform(text1,text2),FadeOut(line1),FadeOut(line2))
+ self.wait(0.5)
+ self.play(ShowCreation(text3))
+ self.wait(1)
+
+
+ v2 = self.add_vector(VECTORS[1],color = BLUE, stroke_width = 3.5)
+ line3 = Line(start = ORIGIN, end = VECTORS[1][0]*RIGHT)
+ line3.set_color(RED_B)
+ line4 = Line(start = line3.get_end(), end = line3.get_end() + VECTORS[1][1]*UP)
+ line4.set_color(GREEN_D)
+ self.play(ShowCreation(line3))
+ self.play(ShowCreation(line4))
+ self.wait(0.5)
+ text4 = TextMobject("(2, 2)",color=BLUE).scale(0.6).shift(1*UP + 1.5*RIGHT)
+ self.play(ShowCreation(text4))
+ text5 = TextMobject(r"$\vec{b}$",color = BLUE).scale(0.8).shift(1*UP + 1.2*RIGHT)
+ text6 = TextMobject(r"\text{$\vec{b}$}",r"\text{=}",r"\text{(1, 1)}").scale(0.7).shift(5.1*LEFT + 1.8*UP)
+ text6[0].set_color(BLUE)
+ text6[2].set_color(BLUE)
+ self.wait(1)
+ self.play(Transform(text4,text5),FadeOut(line3),FadeOut(line4))
+ self.wait(0.5)
+ self.play(ShowCreation(text6))
+ self.wait(2)
+
+
+
+ text7 = TextMobject(r"\text{Scaling}",r"\text{ $\vec{b}$ }",r"\text{by 2 units}",color = GOLD).scale(0.7).shift(2.8*UP+4*RIGHT)
+ text7[1].set_color(BLUE)
+ self.play(ShowCreation(text7))
+ self.play(FadeOut(text4))
+ v3 = self.add_vector(VECTORS[2],color = BLUE, stroke_width = 3.5)
+ line7 = Line(start = ORIGIN, end = VECTORS[2][0]*RIGHT)
+ line7.set_color(RED_B)
+ line8 = Line(start = line7.get_end(), end = line7.get_end() + VECTORS[2][1]*UP)
+ line8.set_color(GREEN_D)
+ self.play(FadeOut(v2))
+ self.play(ShowCreation(line7))
+ self.play(ShowCreation(line8))
+
+
+ self.wait(0.5)
+
+ text8 = TextMobject("(2, 2)",color=BLUE).scale(0.6).shift(2.5*RIGHT + 2*UP)
+ text9 = TextMobject(r"$2\vec{b}$",color = BLUE).scale(0.8).shift(2*UP + 2.3*RIGHT)
+ self.play(ShowCreation(text8))
+ self.wait(1)
+ self.play(Transform(text8,text9),FadeOut(line7),FadeOut(line8))
+ self.wait(1)
+ text10 = TextMobject(r"\text{$2\vec{b}$}",r"\text{=}",r"\text{(2, 2)}").scale(0.7).shift(5.1*LEFT + 1.8*UP)
+ text10[0].set_color(BLUE)
+ text10[2].set_color(BLUE)
+ self.play(Transform(text6,text10))
+ self.wait(1)
+ self.play(FadeOut(text7))
+ self.wait(1.5)
+
+
+
+ text11 = TextMobject(r"Addition of vectors",color = GOLD).scale(0.7).shift(2.8*UP+5*RIGHT)
+ self.play(ShowCreation(text11))
+ v1.move_to(3*UP+2.5*RIGHT)
+ self.play(ShowCreation(v1),FadeOut(text8),FadeOut(text1))
+ v4 = self.add_vector(VECTORS[3],color = ORANGE, stroke_width = 3.5)
+ line7 = Line(start = ORIGIN, end = VECTORS[3][0]*RIGHT)
+ line7.set_color(RED_B)
+ line8 = Line(start = line7.get_end(), end = line7.get_end() + VECTORS[3][1]*UP)
+ line8.set_color(GREEN_D)
+ self.play(ShowCreation(line7))
+ self.play(ShowCreation(line8))
+ text12 = TextMobject("(3, 4)",color=ORANGE).scale(0.6).shift(3.5*RIGHT + 3.8*UP)
+ text13 = TextMobject(r"$\vec{c}$",color = ORANGE).scale(0.8).shift(3.7*UP + 3.3*RIGHT)
+ self.play(ShowCreation(text12))
+ self.wait(1)
+ self.play(Transform(text12,text13),FadeOut(line7),FadeOut(line8))
+ self.wait(1)
+ add = TextMobject("+").scale(0.8).shift(6.2*LEFT + 1.8*UP)
+ line_1= Line().shift(1.5*UP+5.1*LEFT).scale(1.5)
+ line_2= Line().shift(0.8*UP+5.1*LEFT).scale(1.5)
+
+ text14=TextMobject(r"\text{$\vec{c}$}",r"\text{=}",r"\text{$\vec{a}$}",r"\text{+}",r"\text{$2\vec{b}$}",r"\text{=}",r"\text{(3, 4)}").scale(0.7).shift(1.2*UP+5.1*LEFT)
+ text14[0].set_color(ORANGE)
+ text14[2].set_color(YELLOW)
+ text14[4].set_color(BLUE)
+ text14[6].set_color(ORANGE)
+
+
+ self.play(ShowCreation(add),ShowCreation(line_1))
+ self.play(ShowCreation(text14),ShowCreation(line_2))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ def write_stuff(self):
+ self.text = []
+ text = self.text
+
+ text.append(TexMobject(r"\text{Consider the Vector Space }",
+ r"{\mathbb{R}^2}"))
+ self.add_title(text[0], 0.7, animate = True)
+ text.append(TexMobject(r"{\mathbb{R}^2}",
+ tex_to_color_map = {r"{\mathbb{R}^2}": BLUE_E}))
+ text[1].shift(6.5*LEFT+3.5*UP)
+ self.wait(0.5)
+ self.play(Transform(text[0], text[1]))
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
--
cgit
From 623a886ee128c7919e3c6b521812a538a3f17603 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:27:40 +0530
Subject: Add files via upload
---
.../gifs2/Projection_of_vectors_in-3D_plane.mp4 | Bin 0 -> 361410 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection_of_vectors_in-3D_plane.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection_of_vectors_in-3D_plane.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection_of_vectors_in-3D_plane.mp4
new file mode 100644
index 0000000..bdca5f9
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Projection_of_vectors_in-3D_plane.mp4 differ
--
cgit
From b54198b0db47c50f6584eb5e0b9ec54d2c1608b6 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:29:57 +0530
Subject: Add files via upload
---
.../Inner-Product_Spaces/Projection-in-3D-space.py | 31 ++++++++++++++++++++++
1 file changed, 31 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Projection-in-3D-space.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Projection-in-3D-space.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Projection-in-3D-space.py
new file mode 100644
index 0000000..e99202f
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Projection-in-3D-space.py
@@ -0,0 +1,31 @@
+from manimlib.imports import *
+class ThreeDSpace(ThreeDScene):
+
+ def construct(self):
+ axes = ThreeDAxes()
+ axes.set_stroke(width=1,color=GOLD)
+ self.add(axes)
+ self.set_camera_orientation(phi = 70*DEGREES,theta =110*DEGREES)
+ line1 = Line(color = YELLOW,opacity=350,start = ORIGIN,end = [0.5,2,2])
+ self.play(ShowCreation(line1))
+ self.wait(1)
+ line2 = Line(color = BLUE,opacity=350,start = ORIGIN,end = [2,2,-1])
+ self.play(ShowCreation(line2))
+ self.wait(1)
+ line3 = Line(opacity=350,start=axes.c2p(0.5,2,2) ,end=axes.c2p(0.5,1.14,-0.17))
+ self.play(ShowCreation(line3))
+ self.wait(1)
+ line4 = Line(color=RED,opacity=350,start = ORIGIN,end=[0.5,1.14,-0.145])
+ self.play(ShowCreation(line4))
+ self.wait(2)
+ text1 = TextMobject(r"\text{Projection on }",r"\text{$\vec{v}$}",r"\text{ onto }",r"\text{$\vec{u}$}",r"\text{ = }",r"\text{$ |\vec{v}|cos\theta$,}").scale(0.6).shift(4*LEFT+3.5*UP)
+ text1[1].set_color(YELLOW)
+ text1[3].set_color(BLUE)
+ text1[5].set_color(RED)
+ text2 = TextMobject(r"\text{where $\theta$ is the angle between the vectors.}").scale(0.6).shift(4*LEFT+3*UP)
+ self.add_fixed_in_frame_mobjects(text1)
+ self.add_fixed_in_frame_mobjects(text2)
+ self.play(ShowCreation(text1),ShowCreation(text2))
+ self.wait(3)
+
+
--
cgit
From 8cc58b1a6fc3f705759cf789f4dbc6fc247c21a1 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:30:40 +0530
Subject: Delete Inner_Product_Space_Example.py
---
.../Inner_Product_Space_Example.py | 175 ---------------------
1 file changed, 175 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py
deleted file mode 100644
index 1f98bad..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Space_Example.py
+++ /dev/null
@@ -1,175 +0,0 @@
-from manimlib.imports import *
-from scipy import sin,cos
-class Inner_Product_Space_Example(GraphScene):
- CONFIG = {
- "x_min" : 0,
- "x_max" : 5,
- "y_min" : 0,
- "y_max" : 6,
- "y_tick_frequency" : 1,
- "x_tick_frequency" : 1,
- "axes_color":LIGHT_GRAY,
- "x_labeled_nums" : list(range(6)),
- "y_labeled_nums" : list(range(6))
- }
- def construct(self):
- self.setup_axes(animate=True)
- curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2.3,color=RED)
- curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2.3,color=DARK_BLUE)
- curve3 = self.get_graph(lambda x : 1.4, x_min=0,x_max=2.3,color=GREEN)
- text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.77*DOWN+0.55*RIGHT)
-
- text2 = TextMobject(r"$g(x)$").scale(0.5).shift(0.15*DOWN+0.55*RIGHT)
- text3 = TextMobject(r"$h(x)$").scale(0.5).shift(1.03*DOWN+0.55*RIGHT)
-
- self.play(ShowCreation(curve1),ShowCreation(text1))
- self.wait(1)
- self.play(ShowCreation(curve2),ShowCreation(text2))
- self.wait(1)
- self.play(ShowCreation(curve3),ShowCreation(text3))
- self.wait(2)
- curve4 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2.3,color=YELLOW)
- text4 = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(0.6*UP+1*RIGHT)
- self.wait(1.5)
-
- self.play(ShowCreation(curve4),ShowCreation(text4),FadeOut(curve2),FadeOut(text2),FadeOut(curve1),FadeOut(text1))
- self.wait(1.5)
- text5 = TextMobject(r"\text{$<f(x) + g(x), h(x)>$ = ",r"\text{$\int_{a}^{b} (f(x) + g(x))h(x)$ $dx$}").scale(0.57).shift(4*RIGHT+3.5*UP)
- text5[1].set_color(ORANGE)
- self.play(ShowCreation(text5))
-
- curve5 = self.get_graph(lambda x : (sin(x) + x)*1.6, x_min=0,x_max=2.3,color=ORANGE)
- text6 = TextMobject(r"$(f(x) + g(x))\cdot h(x)$").scale(0.5).shift(2.2*UP+1.4*RIGHT)
- area1 = self.get_area(curve5,0,2.3)
- area1.set_color(ORANGE)
- self.wait(1)
- self.play(FadeOut(curve4),FadeOut(text4),FadeOut(curve3),FadeOut(text3),ShowCreation(curve5),ShowCreation(text6),ShowCreation(area1))
- self.wait(2)
- text7 = TextMobject(r"\text{$<f(x), h(x)>$ = ",r"\text{$\int_{a}^{b} (f(x)h(x)$ $dx$}").scale(0.57).shift(5*RIGHT+3*UP)
- text7[1].set_color(BLUE)
- self.play(ShowCreation(text7))
- self.wait(1.5)
- curve6 = self.get_graph(lambda x : (sin(x))*1.6, x_min=0,x_max=2.3,color=BLUE)
- text8 = TextMobject(r"$f(x)\cdot h(x)$").scale(0.5).shift(1.4*DOWN+0.8*RIGHT)
- area2 = self.get_area(curve6,0,2.3)
- self.play(ShowCreation(curve6),ShowCreation(text8),ShowCreation(area2))
- self.wait(1.5)
- text9 = TextMobject(r"\text{$<g(x), h(x)>$ = ",r"\text{$\int_{a}^{b} (g(x)h(x)$ $dx$}").scale(0.57).shift(5*RIGHT+2.5*UP)
- text9[1].set_color(MAROON_B)
- self.play(ShowCreation(text9))
- self.wait(1.5)
- curve7 = self.get_graph(lambda x : x*1.6, x_min=0,x_max=2.3,color=MAROON_B)
- text10 = TextMobject(r"$g(x)\cdot h(x)$").scale(0.5).shift(0.8*RIGHT+1*UP)
- area3 = self.get_area(curve7,0,2.3)
- area3.set_color(MAROON_B)
- self.play(ShowCreation(curve7),ShowCreation(text10),ShowCreation(area3))
- self.wait(2.6)
- curve8 = self.get_graph(lambda x : (sin(x))*1.6 + x*1.6, x_min=0,x_max=2.3,color=RED_C)
- area4 = self.get_area(curve8,0,2.3)
- area4.set_color(RED_C)
- text11 = TextMobject(r"$f(x)h(x) + g(x)h(x)$").scale(0.5).shift(2.2*UP + 1.4*RIGHT)
- self.play(FadeOut(curve6),FadeOut(text8),FadeOut(curve7),FadeOut(text10),FadeOut(area2),FadeOut(area3),ShowCreation(curve8),ShowCreation(area4))
- self.wait(1)
- self.play(Transform(text6,text11))
- self.wait(1.7)
- text12 = TextMobject(r"$<f(x) + g(x), h(x)>$ = $<f(x), h(x)>$ + $<g(x), h(x)>$").scale(0.465).shift(0.7*UP+4*RIGHT)
- rect1 = Rectangle(height=0.5)
- rect1.surround(text12)
- self.play(ShowCreation(text12),ShowCreation(rect1))
- self.wait(3)
- self.play(FadeOut(text6),FadeOut(text5),FadeOut(text7),FadeOut(text9),FadeOut(text12),FadeOut(rect1),FadeOut(curve8),FadeOut(area4),FadeOut(text11),FadeOut(curve5),FadeOut(area1))
-
- curve2.set_color(ORANGE)
- self.play(ShowCreation(curve1),ShowCreation(text1))
- self.wait(1)
- self.play(ShowCreation(curve2),ShowCreation(text2))
- self.wait(2)
- curve9 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2.3,color=GREEN)
- text13 = TextMobject(r"$2f(x)$").scale(0.5).shift(1.1*DOWN+0.55*RIGHT)
- self.play(Transform(curve1,curve9),Transform(text1,text13))
- self.wait(1.5)
-
- text14 = TextMobject(r"\text{$<2f(x), g(x)>$ = ",r"\text{$\int_{a}^{b} (2f(x))g(x)$ $dx$}").scale(0.57).shift(4*RIGHT+3.5*UP)
- text14[1].set_color(YELLOW)
- self.play(ShowCreation(text14))
- self.wait(2.2)
- curve10 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2.3,color=YELLOW)
- text15 = TextMobject(r"$2f(x)\cdot g(x)$").scale(0.5).shift(1*RIGHT+0.97*UP)
- area5 = self.get_area(curve10,0,2.3)
- area5.set_color(YELLOW)
- self.play(ShowCreation(area5),ShowCreation(curve10),ShowCreation(text15),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
- self.wait(2)
- text16 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{a}^{b} f(x)g(x)$ $dx$}").scale(0.57).shift(3.8*RIGHT+2.9*UP)
- text16[1].set_color(TEAL)
- self.play(ShowCreation(text16))
- self.wait(1.7)
- curve11 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2.3,color=TEAL)
- area6 = self.get_area(curve11,0,2.3)
- area6.set_color(TEAL)
- text17 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.9*RIGHT+0.7*DOWN)
- self.play(ShowCreation(curve11),ShowCreation(text17),ShowCreation(area6))
- self.wait(2)
-
- text18 = TextMobject(r"\text{$2 <f(x), g(x)>$ = ",r"\text{$2 \int_{a}^{b} f(x)g(x)$ $dx$}").scale(0.57).shift(4*RIGHT+2.3*UP)
- text18[1].set_color(DARK_BLUE)
- self.play(ShowCreation(text18))
- self.wait(2)
- curve12 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2.3,color=DARK_BLUE)
- area7 = self.get_area(curve12,0,2.3)
- area7.set_color(DARK_BLUE)
- text19 = TextMobject(r"= $2( f(x)\cdot g(x) )$").scale(0.5).shift(2.5*RIGHT+0.97*UP)
- self.play(ShowCreation(curve12),ShowCreation(area7),ShowCreation(text19),FadeOut(text17),FadeOut(area6),FadeOut(curve11))
-
- self.wait(2.5)
- text20 = TextMobject(r"$<2f(x), g(x)>$ = $2<f(x), g(x)>$").scale(0.57).shift(0.6*DOWN+4*RIGHT)
- rect2 = Rectangle(height=0.5)
- rect2.surround(text20)
- self.play(ShowCreation(text20),ShowCreation(rect2))
- self.wait(3)
-
- self.play(FadeOut(text14),FadeOut(text15),FadeOut(text19),FadeOut(text16),FadeOut(text18),FadeOut(rect2),FadeOut(curve10),FadeOut(area5),FadeOut(curve12),FadeOut(area7),FadeOut(text20))
- curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2.3,color=YELLOW)
- text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.77*DOWN+0.55*RIGHT)
- self.play(ShowCreation(curve1),ShowCreation(text1))
- self.wait(1.5)
- self.play(ShowCreation(curve2),ShowCreation(text2))
- self.wait(1.7)
- text21 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{a}^{b} f(x)g(x)$ $dx$}").scale(0.57).shift(3.5*RIGHT+3*UP)
- text21[1].set_color(GREEN)
- self.play(ShowCreation(text21))
- self.wait(2)
- curve13 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2.3,color=GREEN)
- area8 = self.get_area(curve13,0,2.3)
- area8.set_color(GREEN)
- text22 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.8*RIGHT+0.7*DOWN)
- self.play(ShowCreation(curve13),ShowCreation(area8),ShowCreation(text22),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
- self.wait(2.2)
- curve14 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2.3,color=RED)
- area9 = self.get_area(curve14,0,2.3)
- area9.set_color(RED)
- self.play(ShowCreation(curve14),ShowCreation(area9))
- text23 = TextMobject(r"= $\overline{f(x)\cdot g(x)}$").scale(0.5).shift(0.7*DOWN+2.1*RIGHT)
- self.play(ShowCreation(text23))
- self.wait(2)
- text24 = TextMobject(r"For all the real functions").scale(0.5).shift(2*RIGHT+2*UP)
- text25 = TextMobject(r"$<\overline{f(x), g(x)}>$ = $<f(x), g(x)>$").scale(0.5).shift(2*RIGHT+1.4*UP)
- rect3 = Rectangle(height=0.7)
- rect3.surround(text25)
- self.play(ShowCreation(text24),ShowCreation(text25),ShowCreation(rect3))
- self.wait(3)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
cgit
From 88f9fd8860d8bcfa5794a30d00f21c119b266eea Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:31:53 +0530
Subject: Add files via upload
---
.../Inner-Product_Spaces/Inner_Product_Example.py | 182 +++++++++++++++++++++
1 file changed, 182 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py
new file mode 100644
index 0000000..97b9696
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/Inner_Product_Example.py
@@ -0,0 +1,182 @@
+from manimlib.imports import *
+from scipy import sin,cos
+class Inner_Product_Space_Example(GraphScene):
+ CONFIG = {
+ "x_min" : 0,
+ "x_max" : 5,
+ "y_min" : 0,
+ "y_max" : 6,
+ "y_tick_frequency" : 1,
+ "x_tick_frequency" : 1,
+ "axes_color":LIGHT_GRAY,
+ "x_labeled_nums" : list(range(6)),
+ "y_labeled_nums" : list(range(6))
+ }
+ def construct(self):
+ self.setup_axes(animate=True)
+ text = TextMobject(r"$f(x), g(x), h(x) \in C[0, 2]$",color=GOLD).scale(0.5).shift(3.5*UP+5.5*LEFT)
+ fx = TextMobject(r"$f(x)$ = sin(x)",color=GOLD).scale(0.5).shift(3*UP+6*LEFT)
+ gx = TextMobject(r"$g(x)$ = x",color=GOLD).scale(0.5).shift(2.5*UP+6.25*LEFT)
+ hx = TextMobject(r"$h(x)$ = 1.4",color=GOLD).scale(0.5).shift(2*UP+6.2*LEFT)
+
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2,color=RED)
+ curve2 = self.get_graph(lambda x : x, x_min=0,x_max=2,color=DARK_BLUE)
+ curve3 = self.get_graph(lambda x : 1.4, x_min=0,x_max=2,color=GREEN)
+ text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.7*DOWN)
+
+ text2 = TextMobject(r"$g(x)$").scale(0.5).shift(0.34*DOWN)
+ text3 = TextMobject(r"$h(x)$").scale(0.5).shift(1.1*DOWN)
+
+
+ self.play(ShowCreation(text))
+ self.play(ShowCreation(curve1),ShowCreation(text1),ShowCreation(fx))
+ self.wait(1)
+ self.play(ShowCreation(curve2),ShowCreation(text2),ShowCreation(gx))
+ self.wait(1)
+ self.play(ShowCreation(curve3),ShowCreation(text3),ShowCreation(hx))
+ self.wait(2)
+ curve4 = self.get_graph(lambda x : sin(x) + x, x_min=0,x_max=2,color=YELLOW)
+ text4 = TextMobject(r"$f(x) + g(x)$").scale(0.5).shift(0.5*UP+0.5*RIGHT)
+ self.wait(1.5)
+
+ self.play(ShowCreation(curve4),ShowCreation(text4),FadeOut(curve2),FadeOut(text2),FadeOut(curve1),FadeOut(text1))
+ self.wait(1.5)
+ text5 = TextMobject(r"\text{$<f(x) + g(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (f(x) + g(x))h(x)$ $dx$}",r"\text{= 4.78}").scale(0.57).shift(3.3*RIGHT+3.5*UP)
+ text5[1].set_color(ORANGE)
+ self.play(ShowCreation(text5))
+
+ curve5 = self.get_graph(lambda x : (sin(x) + x)*1.6, x_min=0,x_max=2,color=ORANGE)
+ text6 = TextMobject(r"$(f(x) + g(x))\cdot h(x)$").scale(0.5).shift(2.2*UP+0.72*RIGHT)
+ area1 = self.get_area(curve5,0,2)
+ area1.set_color(ORANGE)
+ self.wait(1)
+ self.play(FadeOut(curve4),FadeOut(text4),FadeOut(curve3),FadeOut(text3),ShowCreation(curve5),ShowCreation(text6),ShowCreation(area1))
+ self.wait(2)
+ text7 = TextMobject(r"\text{$<f(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (f(x)h(x)$ $dx$}",r"\text{= 1.98}").scale(0.57).shift(4.5*RIGHT+3*UP)
+ text7[1].set_color(BLUE)
+ self.play(ShowCreation(text7))
+ self.wait(1.5)
+ curve6 = self.get_graph(lambda x : (sin(x))*1.6, x_min=0,x_max=2,color=BLUE)
+ text8 = TextMobject(r"$f(x)\cdot h(x)$").scale(0.5).shift(0.9*DOWN+0.3*RIGHT)
+ area2 = self.get_area(curve6,0,2)
+ self.play(ShowCreation(curve6),ShowCreation(text8),ShowCreation(area2))
+ self.wait(1.5)
+ text9 = TextMobject(r"\text{$<g(x), h(x)>$ = ",r"\text{$\int_{0}^{2} (g(x)h(x)$ $dx$}",r"\text{= 2.8}").scale(0.57).shift(4.5*RIGHT+2.5*UP)
+ text9[1].set_color(MAROON_B)
+ self.play(ShowCreation(text9))
+ self.wait(1.5)
+ curve7 = self.get_graph(lambda x : x*1.6, x_min=0,x_max=2,color=MAROON_B)
+ text10 = TextMobject(r"$g(x)\cdot h(x)$").scale(0.5).shift(0.3*RIGHT+0.78*UP)
+ area3 = self.get_area(curve7,0,2)
+ area3.set_color(MAROON_B)
+ self.play(ShowCreation(curve7),ShowCreation(text10),ShowCreation(area3))
+ self.wait(2.6)
+ curve8 = self.get_graph(lambda x : (sin(x))*1.6 + x*1.6, x_min=0,x_max=2,color=RED_C)
+ area4 = self.get_area(curve8,0,2)
+ area4.set_color(RED_C)
+ text11 = TextMobject(r"$f(x)h(x) + g(x)h(x)$").scale(0.5).shift(2.2*UP + 0.76*RIGHT)
+ self.play(FadeOut(curve6),FadeOut(text8),FadeOut(curve7),FadeOut(text10),FadeOut(area2),FadeOut(area3),ShowCreation(curve8),ShowCreation(area4))
+ self.wait(1)
+ self.play(Transform(text6,text11))
+ self.wait(1.7)
+ text12 = TextMobject(r"$<f(x) + g(x), h(x)>$ = $<f(x), h(x)>$ + $<g(x), h(x)>$").scale(0.465).shift(0.7*UP+4*RIGHT)
+ rect1 = Rectangle(height=0.5)
+ rect1.surround(text12)
+ self.play(ShowCreation(text12),ShowCreation(rect1))
+ self.wait(3)
+ self.play(FadeOut(text6),FadeOut(text5),FadeOut(text7),FadeOut(text9),FadeOut(text12),FadeOut(rect1),FadeOut(curve8),FadeOut(area4),FadeOut(text11),FadeOut(curve5),FadeOut(area1))
+
+ curve2.set_color(ORANGE)
+ self.play(ShowCreation(curve1),ShowCreation(text1))
+ self.wait(1)
+ self.play(ShowCreation(curve2),ShowCreation(text2))
+ self.wait(2)
+ curve9 = self.get_graph(lambda x : 2*sin(x), x_min=0,x_max=2,color=GREEN)
+ text13 = TextMobject(r"$2f(x)$").scale(0.5).shift(0.75*DOWN)
+ self.play(Transform(curve1,curve9),Transform(text1,text13))
+ self.wait(1.5)
+
+ text14 = TextMobject(r"\text{$<2f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} (2f(x))g(x)$ $dx$}",r"\text{= 3.48}").scale(0.57).shift(4*RIGHT+3.5*UP)
+ text14[1].set_color(YELLOW)
+ self.play(ShowCreation(text14))
+ self.wait(2.2)
+ curve10 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2,color=YELLOW)
+ text15 = TextMobject(r"$2f(x)\cdot g(x)$").scale(0.5).shift(0.35*RIGHT+1.03*UP)
+ area5 = self.get_area(curve10,0,2)
+ area5.set_color(YELLOW)
+ self.play(ShowCreation(area5),ShowCreation(curve10),ShowCreation(text15),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
+ self.wait(2)
+ text16 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 1.74}").scale(0.57).shift(3.8*RIGHT+2.9*UP)
+ text16[1].set_color(TEAL)
+ self.play(ShowCreation(text16))
+ self.wait(1.7)
+ curve11 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=TEAL)
+ area6 = self.get_area(curve11,0,2)
+ area6.set_color(TEAL)
+ text17 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.4*RIGHT+0.7*DOWN)
+ self.play(ShowCreation(curve11),ShowCreation(text17),ShowCreation(area6))
+ self.wait(2)
+
+ text18 = TextMobject(r"\text{$2 <f(x), g(x)>$ = ",r"\text{$2 \int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 3.48}").scale(0.57).shift(4*RIGHT+2.3*UP)
+ text18[1].set_color(DARK_BLUE)
+ self.play(ShowCreation(text18))
+ self.wait(2)
+ curve12 = self.get_graph(lambda x : 2*sin(x)*x, x_min=0,x_max=2,color=DARK_BLUE)
+ area7 = self.get_area(curve12,0,2)
+ area7.set_color(DARK_BLUE)
+ text19 = TextMobject(r"= $2( f(x)\cdot g(x) )$").scale(0.5).shift(1.89*RIGHT+1.03*UP)
+ self.play(ShowCreation(curve12),ShowCreation(area7),ShowCreation(text19),FadeOut(text17),FadeOut(area6),FadeOut(curve11))
+
+ self.wait(2.5)
+ text20 = TextMobject(r"$<2f(x), g(x)>$ = $2<f(x), g(x)>$").scale(0.57).shift(0.6*DOWN+4*RIGHT)
+ rect2 = Rectangle(height=0.5)
+ rect2.surround(text20)
+ self.play(ShowCreation(text20),ShowCreation(rect2))
+ self.wait(3)
+
+ self.play(FadeOut(text14),FadeOut(text15),FadeOut(text19),FadeOut(text16),FadeOut(text18),FadeOut(rect2),FadeOut(curve10),FadeOut(area5),FadeOut(curve12),FadeOut(area7),FadeOut(text20))
+ curve1 = self.get_graph(lambda x : sin(x), x_min=0,x_max=2,color=YELLOW)
+ text1 = TextMobject(r"$f(x)$").scale(0.5).shift(1.77*DOWN)
+ self.play(ShowCreation(curve1),ShowCreation(text1))
+ self.wait(1.5)
+ self.play(ShowCreation(curve2),ShowCreation(text2))
+ self.wait(1.7)
+ text21 = TextMobject(r"\text{$<f(x), g(x)>$ = ",r"\text{$\int_{0}^{2} f(x)g(x)$ $dx$}",r"\text{= 1.74}").scale(0.57).shift(3.5*RIGHT+3*UP)
+ text21[1].set_color(GREEN)
+ self.play(ShowCreation(text21))
+ self.wait(2)
+ curve13 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=GREEN)
+ area8 = self.get_area(curve13,0,2)
+ area8.set_color(GREEN)
+ text22 = TextMobject(r"$f(x)\cdot g(x)$").scale(0.5).shift(0.32*RIGHT+0.7*DOWN)
+ self.play(ShowCreation(curve13),ShowCreation(area8),ShowCreation(text22),FadeOut(curve1),FadeOut(text1),FadeOut(curve2),FadeOut(text2))
+ self.wait(2.2)
+ curve14 = self.get_graph(lambda x : sin(x)*x, x_min=0,x_max=2,color=RED)
+ area9 = self.get_area(curve14,0,2)
+ area9.set_color(RED)
+ self.play(ShowCreation(curve14),ShowCreation(area9))
+ text23 = TextMobject(r"= $\overline{f(x)\cdot g(x)}$").scale(0.5).shift(0.7*DOWN+1.7*RIGHT)
+ self.play(ShowCreation(text23))
+ self.wait(2)
+ text24 = TextMobject(r"For all the real functions").scale(0.5).shift(2*RIGHT+2*UP)
+ text25 = TextMobject(r"$<\overline{f(x), g(x)}>$ = $<f(x), g(x)>$").scale(0.5).shift(2*RIGHT+1.4*UP)
+ rect3 = Rectangle(height=0.7)
+ rect3.surround(text25)
+ self.play(ShowCreation(text24),ShowCreation(text25),ShowCreation(rect3))
+ self.wait(3)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
--
cgit
From 5a45e266c3484c6bb2ff46cf68ce67bbfe566ee5 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:32:40 +0530
Subject: Delete Linear_Subspace.py
---
.../Vector-Spaces/Subspaces/Linear_Subspace.py | 42 ----------------------
1 file changed, 42 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
deleted file mode 100644
index 9062b30..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Linear_Subspace.py
+++ /dev/null
@@ -1,42 +0,0 @@
-from manimlib.imports import *
-class Subspace(ThreeDScene):
-
-
- def construct(self):
- axes = ThreeDAxes()
- self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
- self.begin_ambient_camera_rotation(rate=0.09)
- cube = Cube(stroke_width=5,color=WHITE).shift([1.5,1.5,1.5]).scale(1.5)
- cube.set_fill(TEAL)
-
- cube.set_opacity(0.4)
- line = Line(color=MAROON,set_opacity=100).shift([1.5,1.5,1.5]).scale(1.5)
- plane1 = Polygon([0,0,3],[3,0,3],[3,3,0],[0,3,0])
- plane1.set_opacity(0.8)
- plane1.set_fill(YELLOW)
- plane1.set_color(YELLOW)
-
-
- plane2 = Polygon([0,3,3],[3,3,3],[3,0,0],[0,0,0])
- plane2.set_opacity(0.7)
- plane2.set_fill(RED)
- plane2.set_color(RED)
-
- vgroup = VGroup(plane1,plane2,line,cube)
- vgroup.shift([-2,-2,-2])
-
- text = TextMobject(r"\text{The}",r"\text{line}",r"\text{representing the intersection of the two planes is a Subspace.}",opacity = 0.6).scale(0.7).shift(3*UP)
- text[1].set_color(MAROON)
- self.add_fixed_in_frame_mobjects(text)
- self.play(ShowCreation(text))
-
-
- self.play(ShowCreation(cube))
- self.play(ShowCreation(plane1))
- self.play(ShowCreation(plane2))
- self.play(ShowCreation(line))
- self.wait(10)
-
-
-
-
\ No newline at end of file
--
cgit
From 0ddf557bde12f37d6053403e5f4ff16ff863296e Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:33:08 +0530
Subject: Delete Subspace_Example.py
---
.../Vector-Spaces/Subspaces/Subspace_Example.py | 86 ----------------------
1 file changed, 86 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
deleted file mode 100644
index d87cd89..0000000
--- a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Example.py
+++ /dev/null
@@ -1,86 +0,0 @@
-from manimlib.imports import *
-class Subspace_Example(Scene):
- def construct(self):
- sq = Square(side = 2, color=BLACK).shift(2*LEFT)
- sq.set_fill(color=RED,opacity=350)
- line1=Line(color=BLACK).shift(2*LEFT)
- line1.rotate(np.pi/2)
- line2=Line(color=BLACK).shift(2.5*LEFT+0.5*UP)
- line2.scale(0.5)
- line3=Line(color=BLACK).shift(+1.5*LEFT)
- line3.scale(0.5)
- a1=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.7*UP)
- a2=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+0.3*DOWN)
- a3=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*DOWN)
- a4=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+0.5*UP)
- big_rect1 = Rectangle().scale(3.3).shift(0.3*DOWN)
- big_rect1.set_fill(color=GOLD,opacity=350)
-
-
- big_rect2=Rectangle().scale(2.7).shift(0.5*DOWN)
- big_rect2.set_fill(color=GREY,opacity=350)
- vec_space=TextMobject("$Vector Space$",color=BLACK).scale(0.73).shift(4.65*RIGHT+2.6*UP)
- sub=TextMobject(r"$Subspace$",color=BLACK).scale(0.73).shift(3.8*RIGHT+1.7*UP)
- self.play(ShowCreation(big_rect1),ShowCreation(vec_space))
- self.play(ShowCreation(big_rect2),ShowCreation(sub))
- self.play(ShowCreation(sq),ShowCreation(line1),ShowCreation(line2),ShowCreation(line3),ShowCreation(a1),ShowCreation(a2),ShowCreation(a3),ShowCreation(a4))
- rec = Rectangle(color=BLACK).scale(0.5).shift(1*RIGHT)
- rec.rotate(np.pi/2)
- rec.set_fill(color=BLUE,opacity=350)
- line4=Line(color=BLACK).shift(1*RIGHT).rotate(np.pi/2)
- line5=Line(color=BLACK).scale(0.25).shift(0.75*RIGHT)
- line6=Line(color=BLACK).scale(0.25).shift(0.5*DOWN+1.25*RIGHT)
- b1=TextMobject(r"$b_1$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*UP)
- b2=TextMobject(r"$b_2$",color=BLACK).scale(0.5).shift(0.3*RIGHT+0.5*DOWN)
- b3=TextMobject(r"$b_3$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.8*DOWN)
- b4=TextMobject(r"$b_4$",color=BLACK).scale(0.5).shift(1.67*RIGHT+0.5*UP)
- self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
- self.wait(1)
- text1=TextMobject(r"$a_1 + a_2 = a_3 + a_4$",color=BLACK).scale(0.5).shift(2*LEFT+1.5*DOWN)
- text2=TextMobject(r"$b_1 + b_2 = b_3 + b_4$",color=BLACK).scale(0.5).shift(1.5*RIGHT+1.5*DOWN)
- self.play(ShowCreation(text1),ShowCreation(text2))
- self.wait(3)
- self.play(FadeOut(text1),FadeOut(text2))
- rec.shift(3*LEFT+2.01*DOWN)
- line4.shift(3*LEFT+2*DOWN)
- line5.shift(3*LEFT+2*DOWN)
- line6.shift(3*LEFT+2*DOWN)
- b1.shift(3.1*LEFT+2.1*DOWN)
- b2.shift(3.1*LEFT+2.1*DOWN)
- b3.shift(2.9*LEFT+2*DOWN)
- b4.shift(2.9*LEFT+2.3*DOWN)
- self.play(ShowCreation(rec),ShowCreation(line4),ShowCreation(line5),ShowCreation(line6),ShowCreation(b1),ShowCreation(b2),ShowCreation(b3),ShowCreation(b4))
- self.wait(2)
-
- text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
- text3=TextMobject(r"$(a_1 + a_2) + (b_1 + b_2) = (a_3 + a_4) + (b_3 + b_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT+0.5*DOWN)
- text4=TextMobject("Vector Addition",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
- self.play(ShowCreation(text3),ShowCreation(text4))
- self.wait(3)
- rec.set_fill(color=GREY,opacity=350)
- self.play(FadeOut(text3),FadeOut(text4),FadeOut(line4),FadeOut(line5),FadeOut(line6),FadeOut(rec),FadeOut(b4),FadeOut(b3),FadeOut(b2),FadeOut(b1))
- sq1=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*UP)
- sq1.set_fill(color=RED,opacity=350)
- sq2=Square(color=BLACK).scale(0.5).shift(1.5*LEFT+1.5*DOWN)
- sq2.set_fill(color=RED,opacity=350)
- rec1=Rectangle(height=0.5,width=1,color=BLACK).shift(2.5*LEFT+1.2*UP)
- rec1.set_fill(color=RED,opacity=350)
- rec2=Rectangle(height=1.5,width=1,color=BLACK)
- rec2.set_fill(color=RED,opacity=350).shift(2.5*LEFT+1.5*DOWN)
- self.play(ShowCreation(sq1),ShowCreation(sq2),ShowCreation(rec1),ShowCreation(rec2))
- a=TextMobject(r"$a_1$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.2*UP)
- b=TextMobject(r"$a_2$",color=BLACK).scale(0.5).shift(3.4*LEFT+1.4*DOWN)
- c=TextMobject(r"$a_3$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*DOWN)
- d=TextMobject(r"$a_4$",color=BLACK).scale(0.5).shift(0.7*LEFT+1.4*UP)
- self.play(ShowCreation(a),ShowCreation(b),ShowCreation(c),ShowCreation(d))
- self.wait(2.3)
- text4=TextMobject("Scalar Multiplication",color=BLACK).scale(0.8).shift(2.5*RIGHT+0.5*UP)
- text5=TextMobject(r"$\implies 2(a_1 + a_2) = 2(a_3 + a_4)$",color=BLACK).scale(0.5).shift(2*RIGHT+0.5*DOWN)
- text6=TextMobject(r"$(a_1 + a_1) + (a_2 + a_2) = (a_3 + a_3) + (a_4 +a_4)$",color=BLACK).scale(0.5).shift(2.5*RIGHT)
- self.play(ShowCreation(text4),ShowCreation(text5),ShowCreation(text6))
- self.wait(3)
-
-
-
-
-
--
cgit
From 9451877998a75f4044459365531d6b05f776c35a Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:40:32 +0530
Subject: Add files via upload
---
.../Subspaces/Intersection_of_Subspaces.py | 52 ++++++++++++++++++++++
.../Subspaces/Subspace_Non_Example.py | 25 +++++++++++
2 files changed, 77 insertions(+)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py
new file mode 100644
index 0000000..ec82daa
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Intersection_of_Subspaces.py
@@ -0,0 +1,52 @@
+from manimlib.imports import *
+class ThreeDSpace(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+
+
+
+
+ cube = Cube(stroke_width=5,color=WHITE).shift([1.5,1.5,1.5]).scale(1.5)
+ cube.set_fill(TEAL)
+
+ cube.set_opacity(0.4)
+
+
+ plane1 = Polygon([0,0,3],[3,0,3],[3,3,0],[0,3,0])
+ plane1.set_opacity(0.65)
+ plane1.set_fill(PURPLE)
+ plane1.set_color(PURPLE)
+
+
+ plane2 = Polygon([0,3,3],[3,3,3],[3,0,0],[0,0,0])
+ plane2.set_opacity(0.7)
+ plane2.set_fill(RED)
+ plane2.set_color(RED)
+ line = Line(color=YELLOW,set_opacity=100).shift([1.5,1.5,1.5]).scale(1.5)
+
+ vgroup = VGroup(plane1,plane2,line,cube)
+ vgroup.shift([-1,-1,-1])
+
+ dot = Dot(color=BLACK).shift([0.5,0.5,0.5]).scale(1)
+ text = TextMobject(r"\text{The}",r"\text{line}",r"\text{representing the intersection of the two planes is a Subspace.}",opacity = 0.6).scale(0.7).shift(3*UP)
+ text[1].set_color(YELLOW)
+ self.add_fixed_in_frame_mobjects(text)
+ self.play(ShowCreation(text))
+
+
+ self.play(ShowCreation(cube))
+ self.play(ShowCreation(plane1))
+ self.play(ShowCreation(plane2))
+
+ self.play(ShowCreation(line),ShowCreation(dot))
+
+
+ self.wait(15)
+
+
+
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py
new file mode 100644
index 0000000..115a722
--- /dev/null
+++ b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/Subspace_Non_Example.py
@@ -0,0 +1,25 @@
+from manimlib.imports import *
+class ThreeDSpace(ThreeDScene):
+
+
+ def construct(self):
+ axes = ThreeDAxes()
+ self.add(axes)
+ self.set_camera_orientation(phi = 80*DEGREES,theta =110*DEGREES)
+ self.begin_ambient_camera_rotation(rate=0.09)
+ plane1 = Polygon([-1.5,1.5,-1.5],[1.5,1.5,-1.5],[1.5,-1.5,1.5],[-1.5,-1.5,1.5])
+ plane1.set_opacity(0.65)
+ plane1.set_fill(GREEN)
+ plane1.set_color(GREEN)
+
+
+ plane2 = Polygon([-1.5,1.5,1.5],[1.5,1.5,1.5],[1.5,-1.5,-1.5],[-1.5,-1.5,-1.5])
+ plane2.set_opacity(0.7)
+ plane2.set_fill(MAROON_A)
+ plane2.set_color(MAROON_A)
+ line = Line(color=YELLOW,set_opacity=100,start=[1.5,1.2,1.2],end=[-1.5,1.2,1.2])
+
+
+ self.play(ShowCreation(plane1),ShowCreation(plane2),ShowCreation(line))
+ self.wait(10)
+
--
cgit
From f424f33f1885a9e8a5d909e454a90287f0490697 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:41:24 +0530
Subject: Delete Subspace_Example.mp4
---
.../Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4 | Bin 608079 -> 0 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4
deleted file mode 100644
index 46e1f3b..0000000
Binary files a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.mp4 and /dev/null differ
--
cgit
From fcd089b5665ab38cb60a6d4ffc3970985a01e6bf Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:41:40 +0530
Subject: Delete Linear_Subspace.gif
---
.../Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif | Bin 4458192 -> 0 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif
deleted file mode 100644
index bec7e5f..0000000
Binary files a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Linear_Subspace.gif and /dev/null differ
--
cgit
From 0ceeedf13e05696108640c764bd9d33608fce3c0 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:41:55 +0530
Subject: Delete Subspace_Example.gif
---
.../Vector-Spaces/Subspaces/gifs/Subspace_Example.gif | Bin 716776 -> 0 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif
deleted file mode 100644
index ffe71a8..0000000
Binary files a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Example.gif and /dev/null differ
--
cgit
From ca44f005584b966faaadda1a46f7d4cd7d7180cd Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:44:53 +0530
Subject: Add files via upload
---
.../Subspaces/gifs/Intersection_of_Subspaces.mp4 | Bin 0 -> 1112086 bytes
.../Subspaces/gifs/Subspace_Non_Example.mp4 | Bin 0 -> 818876 bytes
2 files changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4
new file mode 100644
index 0000000..d43bfbe
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Intersection_of_Subspaces.mp4 differ
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4
new file mode 100644
index 0000000..390f4cf
Binary files /dev/null and b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Subspaces/gifs/Subspace_Non_Example.mp4 differ
--
cgit
From 46adc3cf03a9198bcd26cbff4344ccca8c7c6c0d Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:46:12 +0530
Subject: Delete Inner_Product_Space_Example.mp4
---
.../gifs2/Inner_Product_Space_Example.mp4 | Bin 3450822 -> 0 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4
deleted file mode 100644
index dee494f..0000000
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--
cgit
From eadaf1b3e4245b4b5f3b932334400c0f3a0dcd22 Mon Sep 17 00:00:00 2001
From: simranchhattani
Date: Sat, 11 Jul 2020 23:48:16 +0530
Subject: Add files via upload
---
.../gifs2/Inner_Product_Space_Example.mp4 | Bin 0 -> 3881235 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4
(limited to 'FSF-2020')
diff --git a/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4 b/FSF-2020/linear-algebra/vector-spaces/Vector-Spaces/Inner-Product_Spaces/gifs2/Inner_Product_Space_Example.mp4
new file mode 100644
index 0000000..edecd88
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--
cgit