From 350ccaf2453180475406256cc8d4c9bfe9db3880 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 02:59:49 +0530
Subject: updated folder name and README.md files
---
.../Orthonormal-Basis/README.md | 30 ++++
.../Orthonormal-Basis/file1_orthogonal.py | 40 +++++
.../file2_sum_of_projections_part1.py | 133 ++++++++++++++++
.../file3_sum_of_projections_part2.py | 173 +++++++++++++++++++++
4 files changed, 376 insertions(+)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
create mode 100755 FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file1_orthogonal.py
create mode 100755 FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py
(limited to 'FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
new file mode 100644
index 0000000..c286736
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
@@ -0,0 +1,30 @@
+# Contributer: Archit Sangal
+My Github Account : architsangal
+
+
+## Sub-Topics Covered:
++ Linear Transformations (Linear Maps)
+
+#### Video 1: Visually understanding linear transformation(using grid)
+
+
+#### Video 2: Linear Transformation when form 1 is given
+
+
+#### Video 3: Matrix Representation Of Linear Transformation
+
+
+#### Video 4: Understand Linear Transformations visually
+
+
+#### Video 5: Uniform Scaling
+
+
+#### Fig.1 Horizontal Shear
+
+
+#### Fig.2 Vertical Shear
+
+
+#### Video 6: Rotation by an angle of in anticlockwise direction
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file1_orthogonal.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file1_orthogonal.py
new file mode 100755
index 0000000..a5d96f5
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file1_orthogonal.py
@@ -0,0 +1,40 @@
+from manimlib.imports import *
+
+class Orthogonal(ThreeDScene):
+ def construct(self):
+ axes = ThreeDAxes()
+ self.play(ShowCreation(axes))
+ self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3)
+
+ text = TextMobject(r"$\hat{i}$",r"$\hat{j}$",r"$\hat{k}$")
+ text[0].move_to(0.7*DOWN+0.8*LEFT)
+ text[1].move_to(0.75*DOWN+0.7*RIGHT)
+ text[2].move_to(0.75*UP+0.4*RIGHT)
+ self.add_fixed_in_frame_mobjects(text)
+ self.play(Write(text))
+
+ line1 = Line(start = ORIGIN,end = RIGHT)
+ line1.set_color(DARK_BLUE)
+ tip1 = Polygon(-0.95*LEFT,-0.8*LEFT-0.1*DOWN,-0.8*LEFT-0.1*UP)
+ tip1.set_opacity(1)
+ tip1.set_fill(DARK_BLUE)
+ tip1.set_color(DARK_BLUE)
+
+ arrow2 = Line(start = ORIGIN,end = UP)
+ arrow2.set_color(DARK_BLUE)
+ tip2 = Polygon(0.95*UP,0.8*UP-0.1*RIGHT,0.8*UP-0.1*LEFT)
+ tip2.set_opacity(1)
+ tip2.set_fill(DARK_BLUE)
+ tip2.set_color(DARK_BLUE)
+ arrow2.set_color(DARK_BLUE)
+
+ arrow3 = Line(start = ORIGIN,end = [0,0,1])
+ arrow3.set_color(DARK_BLUE)
+ tip3 = Polygon([0,0,0.95],[0,0,0.8]-0.1*RIGHT,[0,0,0.8]-0.1*LEFT)
+ tip3.set_opacity(1)
+ tip3.set_fill(DARK_BLUE)
+ tip3.set_color(DARK_BLUE)
+
+ self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3))
+
+ self.wait()
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py
new file mode 100755
index 0000000..81a0888
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py
@@ -0,0 +1,133 @@
+from manimlib.imports import *
+class LinearTrans(LinearTransformationScene):
+ CONFIG = {
+ "show_basis_vectors": True,
+ "basis_vector_stroke_width": 1,
+ "leave_ghost_vectors": False,
+ "show_coordinates": True,
+ }
+
+ def construct(self):
+
+ self.setup()
+
+ matrix = [[0.6,-0.8],[0.8,0.6]]
+ self.apply_matrix(matrix)
+
+ self.wait(2)
+ orthonormal = TextMobject(r"These are 2 orthonormal vectors($v_1$ and $v_2$)")
+ orthonormal.scale(0.7)
+ orthonormal.move_to(DOWN+LEFT*3.5)
+ orthonormal.add_background_rectangle()
+ v1 = TextMobject(r"$v_1$")
+ v1.scale(0.75)
+ v1.set_color(X_COLOR)
+ v1.move_to(0.75*UP+RIGHT)
+ v1.add_background_rectangle()
+ v2 = TextMobject(r"$v_2$")
+ v2.scale(0.75)
+ v2.set_color(Y_COLOR)
+ v2.move_to(0.75*UP+LEFT*1.25)
+ v2.add_background_rectangle()
+ self.play(Write(orthonormal))
+ self.play(Write(v1),Write(v2))
+ self.wait()
+ self.play(FadeOut(orthonormal), FadeOut(v1), FadeOut(v2))
+
+ arrow = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
+ arrow.scale(1.2)
+ arrow.set_color(BLUE)
+ arrow.apply_matrix(matrix)
+ text3 = TextMobject("v")
+ text3.move_to(3.2*UP+1.2*RIGHT)
+ text3.add_background_rectangle()
+ self.play(ShowCreation(arrow),Write(text3))
+ self.wait()
+ v_cor = TextMobject("(1,3)")
+ v_cor.move_to(3.2*UP+1.3*RIGHT)
+ v_cor.set_color(BLUE)
+ v_cor.scale(0.75)
+ v_cor.add_background_rectangle()
+ self.play(Transform(text3,v_cor))
+
+ line1 = DashedLine(start = 1*UP+3*RIGHT, end = 3*RIGHT)
+ line2 = DashedLine(start = 1*UP+3*RIGHT, end = UP)
+ line1.apply_matrix(matrix)
+ line2.apply_matrix(matrix)
+ self.play(ShowCreation(line1),ShowCreation(line2),run_time = 2)
+
+ v1 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
+ v1.scale(1.2)
+ v1.set_color(BLUE)
+ v1.apply_matrix(matrix)
+ arrow1 = Arrow(start = ORIGIN,end = 3*RIGHT)
+ arrow1.scale(1.2)
+ arrow1.set_color("#6B8E23")
+ arrow1.apply_matrix(matrix)
+ self.play(Transform(v1,arrow1))
+ v1_cor = TextMobject(r"$ v_1$")
+ v1_cor.move_to(2.5*UP+3*RIGHT)
+ v1_cor.scale(0.75)
+ v1_cor.add_background_rectangle()
+ self.play(Write(v1_cor))
+ self.wait(0.5)
+ text1 = TextMobject(r"(1.8,2.4)")
+ text1.move_to(2.1*UP+2.5*RIGHT)
+ text1.scale(0.75)
+ text1.set_color("#6B8E23")
+ text1.add_background_rectangle()
+ self.play(Transform(v1_cor,text1))
+
+ v2 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)
+ v2.scale(1.2)
+ v2.set_color("#8b0000")
+ v2.apply_matrix(matrix)
+ arrow2 = Arrow(start = ORIGIN,end = UP)
+ arrow2.scale(2.1)
+ arrow2.set_color("#8b0000")
+ arrow2.apply_matrix(matrix)
+ self.wait(0.5)
+ self.play(Transform(v2,arrow2))
+ self.wait(0.5)
+ v2_cor = TextMobject(r"$ v_2$")
+ v2_cor.move_to(0.75*UP+2.5*LEFT)
+ v2_cor.scale(0.75)
+ v2_cor.add_background_rectangle()
+ self.play(Write(v2_cor))
+ self.wait(0.5)
+ text2 = TextMobject(r"(-0.8,0.6)")
+ text2.move_to(0.75*UP+1.75*LEFT)
+ text2.scale(0.75)
+ text2.set_color("#8b0000")
+ text2.add_background_rectangle()
+ self.play(Transform(v2_cor,text2))
+
+ self.wait()
+
+ self.play(ApplyMethod(v2.move_to,1.4*RIGHT+2.7*UP),FadeOut(v1_cor),FadeOut(v2_cor),FadeOut(v_cor))
+
+ self.wait()
+
+ ending = TextMobject(r"$v = v_1 + v_2$")
+ ending.scale(0.7)
+ ending.move_to(DOWN)
+ ending.add_background_rectangle()
+ self.play(Write(ending))
+ self.wait()
+ self.play(FadeOut(ending))
+
+ ending = TextMobject(r"$\left[ \begin{array} {c} 1\\ 3 \end{array}\right] = \left[ \begin{array} {c}1.8 \\ 2.4 \end{array}\right] + \left[ \begin{array} {c} -0.8\\ 0.6 \end{array}\right]$")
+ ending.scale(0.7)
+ ending.move_to(DOWN)
+ ending.add_background_rectangle()
+ self.play(Write(ending))
+ self.wait()
+ self.play(FadeOut(ending))
+
+ ending = TextMobject(r"$v$ is the sum of projections on the orthonormal vectors")
+ ending.scale(0.7)
+ ending.move_to(DOWN)
+ ending.add_background_rectangle()
+ self.play(Write(ending))
+ self.wait()
+ self.play(FadeOut(ending))
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py
new file mode 100644
index 0000000..9d25192
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py
@@ -0,0 +1,173 @@
+from manimlib.imports import *
+class ThreeDExplanation(ThreeDScene):
+
+ def construct(self):
+
+ text = TextMobject("Let us consider the example discussed above again. These are the things we know:-")
+ text.scale(0.75)
+ self.add_fixed_in_frame_mobjects(text)
+ text.move_to(3*UP)
+ self.play(Write(text))
+ self.wait(2)
+ basis = TextMobject(r"Set of Orthonormal Basis - $\left(\begin{array}{c}\frac{1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}\frac{-1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}0\\0\\1\end{array}\right)$")
+ basis.scale(0.75)
+ basis.move_to(UP*1.5)
+ self.play(Write(basis))
+ v = TextMobject(r"$v_1$",r"$v_2$",r"$v_3$")
+ v[0].move_to(UP*0.5+RIGHT*0.75)
+ v[1].move_to(UP*0.5+RIGHT*2.5)
+ v[2].move_to(UP*0.5+RIGHT*4)
+ eq = TextMobject(r"$v = \left(\begin{array}{c}3\\4\\5\end{array}\right)$")
+ eq1 = TextMobject(r"$ = \frac{3}{\sqrt{2}} + \frac{4}{\sqrt{2}} + 0 = \frac{7}{\sqrt{2}}$")
+ eq2 = TextMobject(r"$ = \frac{-3}{\sqrt{2}} + \frac{4}{\sqrt{2}} + 0 =\frac{1}{\sqrt{2}}$")
+ eq3 = TextMobject(r"$ = 0 + 0 + 5 =5$")
+ eq.move_to(4*LEFT+DOWN)
+ eq1.move_to(0.5*DOWN+2*RIGHT)
+ eq2.move_to(1.5*DOWN+2*RIGHT)
+ eq3.move_to(2.5*DOWN+2*RIGHT)
+ self.play(Write(v))
+ self.play(Write(eq))
+ self.play(Write(eq1))
+ self.play(Write(eq2))
+ self.play(Write(eq3))
+ self.wait()
+ self.play(FadeOut(text), FadeOut(basis), FadeOut(eq), FadeOut(v), FadeOut(eq1), FadeOut(eq2), FadeOut(eq3))
+ self.wait()
+
+ text = TextMobject("These are the 3 mutually orthonormal basis of the set(", r"$v_1$, ", r"$v_2$, ", r"$v_3$",")")
+ text[1].set_color(DARK_BLUE)
+ text[2].set_color(RED)
+ text[3].set_color(YELLOW)
+ text.scale(0.75)
+ self.add_fixed_in_frame_mobjects(text)
+ text.move_to(3*DOWN)
+ self.play(Write(text))
+ self.wait()
+
+ axes = ThreeDAxes(x_min = -9,x_max=9,y_min=-9,y_max=9,z_min=-9,z_max=9)
+ self.play(ShowCreation(axes))
+ self.move_camera(distance = 100, phi=30*DEGREES,theta=45*DEGREES,run_time=3)
+ self.begin_ambient_camera_rotation(rate=0.3)
+
+ dashedline1 = DashedLine(start = -12*(UP+RIGHT), end = 12*(UP+RIGHT))
+ dashedline2 = DashedLine(start = -12*(UP+LEFT), end = 12*(UP+LEFT))
+ dashedline3 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 3.5*UP+3.5*RIGHT)
+ dashedline4 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 0.5*UP+0.5*LEFT)
+ dashedline5 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = [0,0,5])
+
+ self.play(ShowCreation(dashedline1), ShowCreation(dashedline2))
+
+ line1 = Line(start = ORIGIN,end = 0.707*RIGHT + 0.707*UP)
+ line1.set_color(DARK_BLUE)
+ tip1 = Polygon(0.707*RIGHT + 0.707*UP, 0.707*RIGHT + 0.607*UP, 0.607*RIGHT + 0.707*UP)
+ tip1.set_opacity(1)
+ tip1.set_fill(DARK_BLUE)
+ tip1.set_color(DARK_BLUE)
+ self.play(ShowCreation(line1), ShowCreation(tip1))
+
+ line2 = Line(start = ORIGIN,end = 0.707*LEFT + 0.707*UP)
+ line2.set_color(RED)
+ tip2 = Polygon(0.707*LEFT + 0.707*UP, 0.707*LEFT + 0.607*UP, 0.607*LEFT + 0.707*UP)
+ tip2.set_opacity(1)
+ tip2.set_fill(RED)
+ tip2.set_color(RED)
+
+ self.play(ShowCreation(line2), ShowCreation(tip2))
+
+ line3 = Line(start = ORIGIN,end = [0,0,1])
+ line3.set_color(YELLOW)
+ tip3 = Polygon([0,0,1],[0,0,0.8]-0.2*RIGHT,[0,0,0.8]-0.2*LEFT)
+ tip3.set_opacity(1)
+ tip3.set_fill(YELLOW)
+ tip3.set_color(YELLOW)
+ self.play(ShowCreation(line3), ShowCreation(tip3))
+ self.wait()
+
+ self.play(FadeOut(text))
+
+ text = TextMobject("Take the projection of ", r"$v$", " on the mutually orthonormal vectors")
+ text[1].set_color(GOLD_E)
+ text.scale(0.75)
+ self.add_fixed_in_frame_mobjects(text)
+ text.move_to(3*DOWN)
+ self.play(Write(text))
+ self.wait(2)
+
+ a_line = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+ a_line.set_color(GOLD_E)
+ a_tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+ a_tip.set_opacity(1)
+ a_tip.set_fill(GOLD_E)
+ a_tip.set_color(GOLD_E)
+
+ self.play(ShowCreation(a_line), ShowCreation(a_tip))
+ self.wait(9)
+ self.play(ShowCreation(dashedline3),ShowCreation(dashedline4),ShowCreation(dashedline5))
+ self.wait(6)
+
+ pv1 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+ pv1.set_color(GOLD_E)
+ pv1tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+ pv1tip.set_opacity(1)
+ pv1tip.set_fill(GOLD_E)
+ pv1tip.set_color(GOLD_E)
+
+ v1_p = Line(start = ORIGIN,end = 3.5*RIGHT + 3.5*UP)
+ v1_p.set_color(BLUE_E)
+ v1_p_tip = Polygon(3.5*RIGHT + 3.5*UP, 3.5*RIGHT + 3.4*UP, 3.4*RIGHT + 3.5*UP)
+ v1_p_tip.set_opacity(1)
+ v1_p_tip.set_fill(BLUE_E)
+ v1_p_tip.set_color(BLUE_E)
+
+ pv2 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+ pv2.set_color(GOLD_E)
+ pv2tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+ pv2tip.set_opacity(1)
+ pv2tip.set_fill(GOLD_E)
+ pv2tip.set_color(GOLD_E)
+
+ v2_p = Line(start = ORIGIN,end = 0.5*LEFT + 0.5*UP)
+ v2_p.set_color(RED_E)
+ v2_p_tip = Polygon(0.5*LEFT + 0.5*UP, 0.5*LEFT + 0.4*UP, 0.4*LEFT + 0.5*UP)
+ v2_p_tip.set_opacity(1)
+ v2_p_tip.set_fill(RED_E)
+ v2_p_tip.set_color(RED_E)
+
+ pv3 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+ pv3.set_color(GOLD_E)
+ pv3tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+ pv3tip.set_opacity(1)
+ pv3tip.set_fill(GOLD_E)
+ pv3tip.set_color(GOLD_E)
+
+ v3_p = Line(start = ORIGIN,end = [0,0,5])
+ v3_p.set_color(YELLOW_E)
+ v3_p_tip = Polygon([0,0,5],[0,0,4.8]+0.2*RIGHT,[0,0,4.8]+0.2*LEFT)
+ v3_p_tip.set_opacity(1)
+ v3_p_tip.set_fill(YELLOW_E)
+ v3_p_tip.set_color(YELLOW_E)
+
+ self.stop_ambient_camera_rotation()
+ self.play(Transform(pv1,v1_p), Transform(pv1tip,v1_p_tip), Transform(pv2,v2_p), Transform(pv2tip,v2_p_tip), Transform(pv3,v3_p), Transform(pv3tip,v3_p_tip))
+ self.play(FadeOut(dashedline1),
+ FadeOut(dashedline2),
+ FadeOut(dashedline3),
+ FadeOut(dashedline4),
+ FadeOut(dashedline5),
+ FadeOut(line1),
+ FadeOut(tip1),
+ FadeOut(line2),
+ FadeOut(tip2),
+ FadeOut(line3),
+ FadeOut(tip3),
+ FadeOut(text))
+
+ text = TextMobject(r"$v$ is the sum of projections on the orthonormal vectors")
+ text.set_color(GOLD_E)
+ text.scale(0.75)
+ self.add_fixed_in_frame_mobjects(text)
+ text.move_to(3*DOWN)
+ self.play(Write(text), ApplyMethod(pv2.move_to,(3.5*RIGHT + 3.5*UP+3*RIGHT+4*UP)/2), ApplyMethod(pv2tip.move_to,(3.1*RIGHT + 3.9*UP)))
+ self.play(ApplyMethod(pv3.move_to,3*RIGHT + 4*UP + [0,0,2.5]), ApplyMethod(pv3tip.move_to,(3*RIGHT + 4*UP + [0,0,4.8])))
+
+ self.wait(3)
\ No newline at end of file
--
cgit
From cb8944b427c93bff78b9b4d4b172613135726ee1 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 03:11:35 +0530
Subject: updated folder name and README.md files
---
.../Orthonormal-Basis/README.md | 29 +++++----------------
.../Orthonormal-Basis/file4.gif | Bin 0 -> 1733367 bytes
.../Orthonormal-Basis/file5.gif | Bin 0 -> 43092116 bytes
.../Orthonormal-Basis/file6.gif | Bin 0 -> 37493895 bytes
4 files changed, 7 insertions(+), 22 deletions(-)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file4.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif
(limited to 'FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
index c286736..55aba66 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
@@ -3,28 +3,13 @@ My Github Account : architsangal
## Sub-Topics Covered:
-+ Linear Transformations (Linear Maps)
++ Orthonormal Bases
-#### Video 1: Visually understanding linear transformation(using grid)
-
+#### Video 1: Example of Orthonormal bases
+
-#### Video 2: Linear Transformation when form 1 is given
-
+#### Video 2: Adding the projections of a vector on orthonormal basis will produce the same vector
+
-#### Video 3: Matrix Representation Of Linear Transformation
-
-
-#### Video 4: Understand Linear Transformations visually
-
-
-#### Video 5: Uniform Scaling
-
-
-#### Fig.1 Horizontal Shear
-
-
-#### Fig.2 Vertical Shear
-
-
-#### Video 6: Rotation by an angle of in anticlockwise direction
-
\ No newline at end of file
+#### Video 3: Relating the example and the property
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file4.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file4.gif
new file mode 100644
index 0000000..4891350
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file4.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif
new file mode 100644
index 0000000..47fc316
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif
new file mode 100644
index 0000000..d4ae50c
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--
cgit
From d6bd3ca38c24960ada366e720784adfb1ed1d77c Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 16 Jul 2020 08:51:02 +0530
Subject: Archit Sangal
---
.../file2_sum_of_projections_part1.py | 6 +++---
.../Orthonormal-Basis/file5.gif | Bin 43092116 -> 5430037 bytes
2 files changed, 3 insertions(+), 3 deletions(-)
(limited to 'FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py
index 81a0888..141e99b 100755
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py
@@ -43,7 +43,7 @@ class LinearTrans(LinearTransformationScene):
text3.add_background_rectangle()
self.play(ShowCreation(arrow),Write(text3))
self.wait()
- v_cor = TextMobject("(1,3)")
+ v_cor = TextMobject("(1 , 3)")
v_cor.move_to(3.2*UP+1.3*RIGHT)
v_cor.set_color(BLUE)
v_cor.scale(0.75)
@@ -71,7 +71,7 @@ class LinearTrans(LinearTransformationScene):
v1_cor.add_background_rectangle()
self.play(Write(v1_cor))
self.wait(0.5)
- text1 = TextMobject(r"(1.8,2.4)")
+ text1 = TextMobject("(1.8 , 2.4)")
text1.move_to(2.1*UP+2.5*RIGHT)
text1.scale(0.75)
text1.set_color("#6B8E23")
@@ -95,7 +95,7 @@ class LinearTrans(LinearTransformationScene):
v2_cor.add_background_rectangle()
self.play(Write(v2_cor))
self.wait(0.5)
- text2 = TextMobject(r"(-0.8,0.6)")
+ text2 = TextMobject("(-0.8 , 0.6)")
text2.move_to(0.75*UP+1.75*LEFT)
text2.scale(0.75)
text2.set_color("#8b0000")
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif
index 47fc316..d7eb0bc 100644
Binary files a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif and b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif differ
--
cgit
From b5eaf0dc784aa69de358c96189cb4a83837939d3 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 16 Jul 2020 11:22:24 +0530
Subject: Archit Sangal
---
.../file3_sum_of_projections_part2.py | 46 +++++++++++++---------
1 file changed, 27 insertions(+), 19 deletions(-)
(limited to 'FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py
index 9d25192..2899286 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py
@@ -3,12 +3,6 @@ class ThreeDExplanation(ThreeDScene):
def construct(self):
- text = TextMobject("Let us consider the example discussed above again. These are the things we know:-")
- text.scale(0.75)
- self.add_fixed_in_frame_mobjects(text)
- text.move_to(3*UP)
- self.play(Write(text))
- self.wait(2)
basis = TextMobject(r"Set of Orthonormal Basis - $\left(\begin{array}{c}\frac{1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}\frac{-1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}0\\0\\1\end{array}\right)$")
basis.scale(0.75)
basis.move_to(UP*1.5)
@@ -31,7 +25,7 @@ class ThreeDExplanation(ThreeDScene):
self.play(Write(eq2))
self.play(Write(eq3))
self.wait()
- self.play(FadeOut(text), FadeOut(basis), FadeOut(eq), FadeOut(v), FadeOut(eq1), FadeOut(eq2), FadeOut(eq3))
+ self.play(FadeOut(basis), FadeOut(eq), FadeOut(v), FadeOut(eq1), FadeOut(eq2), FadeOut(eq3))
self.wait()
text = TextMobject("These are the 3 mutually orthonormal basis of the set(", r"$v_1$, ", r"$v_2$, ", r"$v_3$",")")
@@ -44,13 +38,20 @@ class ThreeDExplanation(ThreeDScene):
self.play(Write(text))
self.wait()
- axes = ThreeDAxes(x_min = -9,x_max=9,y_min=-9,y_max=9,z_min=-9,z_max=9)
+ axes = ThreeDAxes(x_min = -6,x_max=6,y_min=-6,y_max=6,z_min=-6,z_max=6)
self.play(ShowCreation(axes))
- self.move_camera(distance = 100, phi=30*DEGREES,theta=45*DEGREES,run_time=3)
- self.begin_ambient_camera_rotation(rate=0.3)
-
- dashedline1 = DashedLine(start = -12*(UP+RIGHT), end = 12*(UP+RIGHT))
- dashedline2 = DashedLine(start = -12*(UP+LEFT), end = 12*(UP+LEFT))
+ self.move_camera(distance = 100, phi=45*DEGREES,theta=45*DEGREES,run_time=5)
+ self.begin_ambient_camera_rotation(rate=0.1)
+
+ xy_plane = Polygon(6*RIGHT+6*UP,-6*RIGHT+6*UP,-6*RIGHT-6*UP,6*RIGHT-6*UP)
+ xy_plane.set_color("#333333")
+ xy_plane.set_fill("#333333")
+ xy_plane.set_opacity(1)
+ xy_plane.fade(0.7)
+ self.play(ShowCreation(xy_plane))
+
+ dashedline1 = DashedLine(start = -6*(UP+RIGHT), end = 6*(UP+RIGHT))
+ dashedline2 = DashedLine(start = -6*(UP+LEFT), end = 6*(UP+LEFT))
dashedline3 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 3.5*UP+3.5*RIGHT)
dashedline4 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 0.5*UP+0.5*LEFT)
dashedline5 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = [0,0,5])
@@ -95,15 +96,17 @@ class ThreeDExplanation(ThreeDScene):
a_line = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
a_line.set_color(GOLD_E)
- a_tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+ a_tip = Polygon(3.92*UP+2.94*RIGHT+[0,0,4.9],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
a_tip.set_opacity(1)
a_tip.set_fill(GOLD_E)
a_tip.set_color(GOLD_E)
self.play(ShowCreation(a_line), ShowCreation(a_tip))
- self.wait(9)
+ self.stop_ambient_camera_rotation()
+ self.move_camera(distance = 100, phi=45*DEGREES,theta=135*DEGREES,run_time=5)
+
self.play(ShowCreation(dashedline3),ShowCreation(dashedline4),ShowCreation(dashedline5))
- self.wait(6)
+ self.wait()
pv1 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
pv1.set_color(GOLD_E)
@@ -142,13 +145,18 @@ class ThreeDExplanation(ThreeDScene):
v3_p = Line(start = ORIGIN,end = [0,0,5])
v3_p.set_color(YELLOW_E)
- v3_p_tip = Polygon([0,0,5],[0,0,4.8]+0.2*RIGHT,[0,0,4.8]+0.2*LEFT)
+ v3_p_tip = Polygon([0,0,5.15],[0,0,4.8]+0.2*RIGHT,[0,0,4.8]+0.2*LEFT)
v3_p_tip.set_opacity(1)
v3_p_tip.set_fill(YELLOW_E)
v3_p_tip.set_color(YELLOW_E)
- self.stop_ambient_camera_rotation()
- self.play(Transform(pv1,v1_p), Transform(pv1tip,v1_p_tip), Transform(pv2,v2_p), Transform(pv2tip,v2_p_tip), Transform(pv3,v3_p), Transform(pv3tip,v3_p_tip))
+ #self.stop_ambient_camera_rotation()
+ self.play(Transform(pv1,v1_p),
+ Transform(pv1tip,v1_p_tip),
+ Transform(pv2,v2_p),
+ Transform(pv2tip,v2_p_tip),
+ Transform(pv3,v3_p),
+ Transform(pv3tip,v3_p_tip))
self.play(FadeOut(dashedline1),
FadeOut(dashedline2),
FadeOut(dashedline3),
--
cgit
From cc8c79fc58c03c734d9e1c8c57da55878a4ffec6 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 16 Jul 2020 11:43:28 +0530
Subject: Archit Sangal
---
.../Orthonormal-Basis/file6.gif | Bin 37493895 -> 21739496 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
(limited to 'FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif
index d4ae50c..1df6413 100644
Binary files a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif and b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif differ
--
cgit
From d5f9e76347842897a50fe7b0d265d8473506a0e6 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Fri, 17 Jul 2020 22:29:51 +0530
Subject: Archit Sangal
---
.../linear-algebra/linear-transformations/Orthonormal-Basis/README.md | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
(limited to 'FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
index 55aba66..e287fa1 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md
@@ -1,5 +1,5 @@
# Contributer: Archit Sangal
-My Github Account : architsangal
+My Github Account : architsangal (https://github.com/architsangal)
## Sub-Topics Covered:
--
cgit