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-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md2
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py46
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py48
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gifbin26037424 -> 17680572 bytes
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gifbin5378916 -> 6343293 bytes
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md2
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gifbin50836502 -> 52608896 bytes
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gifbin19348496 -> 31583525 bytes
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py34
-rwxr-xr-xFSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py15
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/README.md2
-rwxr-xr-xFSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file2_sum_of_projections_part1.py6
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file3_sum_of_projections_part2.py46
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gifbin43092116 -> 5430037 bytes
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gifbin37493895 -> 21739496 bytes
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/README.md2
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md4
-rw-r--r--FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md2
18 files changed, 133 insertions, 76 deletions
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md
index 0305ba7..832aa5d 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md
@@ -1,5 +1,5 @@
# Contributer: Archit Sangal
-My Github Account : <a href="https://github.com/architsangal">architsangal</a>
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal)
<br/></br>
## Sub-Topics Covered:
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py
index af51fc6..a74b641 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py
@@ -6,7 +6,7 @@ class Algo(ThreeDScene):
axes = ThreeDAxes(x_min = -5,x_max=5,y_min=-3,y_max=3,z_min=-4,z_max=4)
self.play(ShowCreation(axes))
- text = TextMobject(r"This is the vector $\beta_1(=\left[\begin{array}{c} 4\\0\\0 \end{array}\right])$")
+ text = TextMobject(r"This is the vector $\beta_1 =\left[\begin{array}{c} 4\\0\\0 \end{array}\right]$")
text.set_color(GREEN)
text.scale(0.6)
text.move_to(3*UP+5*LEFT)
@@ -42,7 +42,7 @@ class Algo(ThreeDScene):
self.wait()
self.play(FadeOut(text))
- text = TextMobject(r"Consider another vector $\beta_2(=\left[\begin{array}{c} 2\\2\\0 \end{array}\right])$")
+ text = TextMobject(r"Consider another vector $\beta_2=\left[\begin{array}{c} 2\\2\\0 \end{array}\right]$")
text1 = TextMobject(r"which is linearly independent to $\beta_1$")
text.set_color(GREEN)
text1.set_color(GREEN)
@@ -141,15 +141,15 @@ class Algo(ThreeDScene):
self.add_fixed_orientation_mobjects(axis[1])
#############################################################################
- text = TextMobject(r"These are the same two orthonormal vectors $\alpha_{1}$ and $\alpha_{2}$")
- text.scale(0.6)
- text.set_color(DARK_BLUE)
- self.add_fixed_in_frame_mobjects(text)
- text.move_to(3*(DOWN+RIGHT))
- self.play(Write(text))
+ self.move_camera(phi=70*DEGREES,theta=30*DEGREES,run_time=3)
+ xy_plane = Polygon(5*RIGHT+3*UP,-5*RIGHT+3*UP,-5*RIGHT-3*UP,5*RIGHT-3*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))
- self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3)
- self.begin_ambient_camera_rotation(rate=0.3)
+ #self.begin_ambient_camera_rotation(rate=0.1)
line1 = Line(start = ORIGIN,end = 1*RIGHT)
line1.set_color(DARK_BLUE)
@@ -183,9 +183,9 @@ class Algo(ThreeDScene):
a_tip_c1.set_fill(GOLD_E)
a_tip_c1.set_color(GOLD_E)
- self.play(FadeOut(text), ShowCreation(a_line), ShowCreation(a_tip), ShowCreation(a_line_c1), ShowCreation(a_tip_c1))
+ self.play(ShowCreation(a_line), ShowCreation(a_tip), ShowCreation(a_line_c1), ShowCreation(a_tip_c1))
- text = TextMobject(r"Now, we have a vector $\beta_3(=\left[\begin{array}{c} 2\\2\\2 \end{array}\right])$")
+ text = TextMobject(r"Now, we have a vector $\beta_3=\left[\begin{array}{c} 2\\2\\2 \end{array}\right]$")
text.set_color(GOLD_E)
text.scale(0.7)
self.add_fixed_in_frame_mobjects(text)
@@ -197,8 +197,8 @@ class Algo(ThreeDScene):
p_line1 = Line(start = ORIGIN,end = 2*RIGHT)
p_line1.set_color(GOLD_E)
- p_tip1 = Polygon(RIGHT,0.8*RIGHT+0.2*DOWN,0.8*RIGHT+0.2*UP)
- p_tip1.move_to(2*RIGHT)
+ p_tip1 = Polygon(2*RIGHT,1.8*RIGHT+0.2*DOWN,1.8*RIGHT+0.2*UP)
+
p_tip1.set_opacity(1)
p_tip1.set_fill(GOLD_E)
p_tip1.set_color(GOLD_E)
@@ -211,6 +211,7 @@ class Algo(ThreeDScene):
self.add_fixed_in_frame_mobjects(text)
text.move_to(3*(DOWN+RIGHT))
self.play(Write(text))
+ self.begin_ambient_camera_rotation(rate=0.05)
self.wait()
self.play(FadeOut(text))
@@ -241,6 +242,7 @@ class Algo(ThreeDScene):
self.add_fixed_in_frame_mobjects(text)
text.move_to(3*(DOWN+RIGHT))
self.play(Write(text))
+
self.play(ShowCreation(o_line1), ShowCreation(o_tip1))
self.wait(2)
self.play(FadeOut(a_line_c1), FadeOut(a_tip_c1),
@@ -266,7 +268,7 @@ class Algo(ThreeDScene):
last_a_tip.set_fill(PURPLE_E)
last_a_tip.set_color(PURPLE_E)
- self.wait()
+ self.wait(5)
text = TextMobject(r"Take projection on $\alpha_2$")
text.scale(0.6)
text.set_color(GOLD_E)
@@ -283,7 +285,7 @@ class Algo(ThreeDScene):
self.add_fixed_in_frame_mobjects(text)
text.move_to(3*DOWN+3.5*RIGHT)
self.play(Write(text))
- self.play(ShowCreation(o_line1), ShowCreation(o_tip1))
+ #self.play(ShowCreation(o_line1), ShowCreation(o_tip1))
self.wait(2)
self.play(ShowCreation(last_a_tip), ShowCreation(last_a))
self.wait()
@@ -299,16 +301,16 @@ class Algo(ThreeDScene):
self.play(FadeOut(o_line1), FadeOut(o_tip1), FadeOut(a_line1_c1), FadeOut(a_tip1_c1), Transform(last_a,larrow3), Transform(last_a_tip,ltip3))
text = TextMobject(r"Normalize, the vector")
- text1 = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$")
+ text1 = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2)$")
text.set_color(PURPLE_E)
text1.set_color(PURPLE_E)
- text.scale(0.6)
- text1.scale(0.6)
+ text.scale(0.55)
+ text1.scale(0.55)
self.add_fixed_in_frame_mobjects(text)
- self.add_fixed_in_frame_mobjects(text1)
text.move_to(3*DOWN+3*RIGHT)
- text1.move_to(3.5*DOWN+3*RIGHT)
+ text1.move_to(3.5*DOWN+3.25*RIGHT)
self.play(Write(text))
+ self.add_fixed_in_frame_mobjects(text1)
self.play(Write(text1))
arrow3 = Line(start = ORIGIN,end = [0,0,1])
@@ -330,4 +332,4 @@ class Algo(ThreeDScene):
text.move_to(3*DOWN+3.5*RIGHT)
self.play(Write(text))
- self.wait(3) \ No newline at end of file
+ self.wait(8)
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py
index 6410a2c..1d23aa2 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py
@@ -3,13 +3,6 @@ from manimlib.imports import *
class NSB(ThreeDScene):
def construct(self):
- axes = ThreeDAxes(x_min = -4,x_max=4,y_min=-4,y_max=4,z_min=-4,z_max=4)
- self.play(ShowCreation(axes))
- self.move_camera(phi=60*DEGREES,theta=45*DEGREES,run_time=3)
- self.begin_ambient_camera_rotation(rate=0.5)
-
- matrix = [[0.577,0.577,0.577],[-0.577,0.577,0.577],[0.577,-0.577,0.577]]
-
line1 = Line(start = ORIGIN,end = 1*RIGHT)
line1.set_color(DARK_BLUE)
tip1 = Polygon(RIGHT,0.9*RIGHT-0.1*DOWN,0.9*RIGHT-0.1*UP)
@@ -32,14 +25,39 @@ class NSB(ThreeDScene):
tip3.set_fill(DARK_BLUE)
tip3.set_color(DARK_BLUE)
- line1.apply_matrix(matrix)
- tip1.apply_matrix(matrix)
- arrow2.apply_matrix(matrix)
- tip2.apply_matrix(matrix)
- arrow3.apply_matrix(matrix)
- tip3.apply_matrix(matrix)
+ axes = ThreeDAxes(x_min = -3,x_max=3,y_min=-3,y_max=3,z_min=-3,z_max=3)
+ self.play(ShowCreation(axes))
+ self.move_camera(phi=70*DEGREES,theta=0*DEGREES,run_time=3)
+ self.begin_ambient_camera_rotation(rate=0.2)
- self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), ShowCreation(arrow3), ShowCreation(tip3))
+ #matrix = [[1,0,0],[0,1,0],[0,0,1]]
+ matrix = [[0.70710678118,-0.57735026919,-0.57735026919],[0.70710678118,0.57735026919,0.57735026919],[0,-0.57735026919,0.57735026919]]
+ matrix1 = [[0.70710678118,0,0],[0.70710678118,1,0],[0,0,1]]
+
+ matrix1 = [[0.70710678118,-0.70710678118,0],[0.70710678118,0.70710678118,0],[0,0,1]]
+ matrix2 = [[1,0,0],[0,0.70710678118,0.70710678118],[0,-0.70710678118,0.70710678118]]
+
+
+ line1.apply_matrix(matrix1)
+ tip1.apply_matrix(matrix1)
+ arrow2.apply_matrix(matrix1)
+ tip2.apply_matrix(matrix1)
+ arrow3.apply_matrix(matrix1)
+ tip3.apply_matrix(matrix1)
+
+ line1.apply_matrix(matrix2)
+ tip1.apply_matrix(matrix2)
+ arrow2.apply_matrix(matrix2)
+ tip2.apply_matrix(matrix2)
+ arrow3.apply_matrix(matrix2)
+ tip3.apply_matrix(matrix2)
+
+ self.play(ShowCreation(line1),
+ ShowCreation(tip1),
+ ShowCreation(arrow2),
+ ShowCreation(tip2),
+ ShowCreation(arrow3),
+ ShowCreation(tip3))
text = TextMobject(r"This is also a set of Orthonormal Vectors")
text.set_color(DARK_BLUE)
@@ -48,4 +66,4 @@ class NSB(ThreeDScene):
text.move_to(3*DOWN+3.5*RIGHT)
self.play(Write(text))
- self.wait(7) \ No newline at end of file
+ self.wait(22)
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif
index 2ce3577..cdc0f2d 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif
Binary files differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif
index 7cd7b3d..e03f265 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif
Binary files differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md
index c286736..2a46424 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md
@@ -1,5 +1,5 @@
# Contributer: Archit Sangal
-My Github Account : <a href="https://github.com/architsangal">architsangal</a>
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal)
<br/></br>
## Sub-Topics Covered:
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif
index e9f4b08..d8c64b7 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif
Binary files differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif
index 683f586..92bdff6 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif
Binary files differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py
index 677f890..0182bd9 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file1_transformations.py
@@ -2,16 +2,20 @@ from manimlib.imports import *
class text(Scene):
def construct(self):
- text1 = TextMobject("For a grid, undergoing a linear transformation, all it's straight lines")
+ text1 = TextMobject("For a grid, undergoing a linear transformation, all its straight lines")
text1.scale(0.9)
text2 = TextMobject("must either remain straight lines or sends to a point in the grid formed")
text2.scale(0.9)
+ text3 = TextMobject("Origin must remain where it was before transformation.")
+ text3.scale(0.9)
text1.move_to(ORIGIN+UP)
text2.move_to(ORIGIN)
+ text3.move_to(ORIGIN+DOWN)
self.play(Write(text1))
self.play(Write(text2))
+ self.play(Write(text3))
self.wait()
- self.play(FadeOut(text1),FadeOut(text2))
+ self.play(FadeOut(text1),FadeOut(text2),FadeOut(text3))
class LinearTransformation(LinearTransformationScene):
CONFIG = {
@@ -34,6 +38,7 @@ class NonLinearTransformation(Scene):
def construct(self):
grid = NumberPlane()
self.play(ShowCreation(grid),run_time =2)
+ # I have taken reference from purusharth's code
NonLinearTrans = lambda coordinates : coordinates + np.array([np.sin(coordinates[1]),np.sin(coordinates[0]),0,])
grid.prepare_for_nonlinear_transform()
self.play(grid.apply_function,NonLinearTrans)
@@ -42,4 +47,27 @@ class NonLinearTransformation(Scene):
text[1].move_to(1.5*DOWN+4*LEFT)
text.add_background_rectangle()
self.play(Write(text))
- self.wait() \ No newline at end of file
+ self.wait()
+
+class MoveOrigin(LinearTransformationScene):
+
+ CONFIG = {
+ "show_basis_vectors": False,
+ }
+ def construct(self):
+ self.wait()
+
+ dot = Dot(ORIGIN, color = YELLOW)
+ self.add_transformable_mobject(dot)
+ self.apply_nonlinear_transformation(self.func)
+ text = TextMobject("This is also not a linear transformation as the origin moves from its original position")
+ text.move_to(2*DOWN)
+ text.scale(0.5)
+ text.set_color(YELLOW)
+ text.add_background_rectangle()
+ self.play(Write(text))
+ self.wait()
+
+ def func(self, point):
+ matrix_transform = self.get_matrix_transformation([[1, -1], [1, 1]])
+ return matrix_transform(point) + UP+ RIGHT
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py
index 96e456d..1f6badd 100755
--- a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file2_before_matrix.py
@@ -69,7 +69,7 @@ class Linear(GraphScene):
class withgrid(LinearTransformationScene):
def construct(self):
- heading = TextMobject(r"Now, Imagine this happening for all the vectors")
+ heading = TextMobject(r"Now, imagine this happening for all the points")
heading.scale(0.5)
heading.move_to(UP*2.5+LEFT*4)
self.play(Write(heading))
@@ -141,6 +141,7 @@ class ThreeDExplanation(ThreeDScene):
text = TextMobject(r"$T(x,y) = (x+y,x-y,x+2y)$")
text.scale(0.75)
text.move_to(UP*2.5+LEFT*4)
+ text.move_to(-UP*3+LEFT*4)
self.add_fixed_in_frame_mobjects(text)
self.play(Write(text))
self.wait()
@@ -218,15 +219,15 @@ class ThreeDExplanation(ThreeDScene):
self.wait(3)
self.stop_ambient_camera_rotation()
- ending = TextMobject(r"$T(\left[\begin{array}{c}x \\ y\end{array}\right]) = \left[\begin{array}{c} x+y \\ x-y \\ x+2y \end{array}\right]$")
+ ending = TextMobject(r"$T(\left[\begin{array}{c}x \\ y\end{array}\right])$ = ",r"$\left[\begin{array}{c} x+y \\ x-y\\ x+2y \end{array}\right]$") #\begin{array}{c} x+y \\ x-y -- \\ x+2y -- \end{array}\right]$")
ending.scale(0.75)
- ending.move_to(-UP*2+LEFT*4)
- self.play(Transform(text,ending))
+ ending.move_to(-UP*3+LEFT*4)
self.add_fixed_in_frame_mobjects(ending)
+ self.play(FadeOut(text),Write(ending))
self.play(FadeOut(plane))
- self.wait(3)
+ self.wait(2)
- self.begin_ambient_camera_rotation(rate=0.5)
- self.wait(5)
+ self.begin_ambient_camera_rotation(rate=0.3)
+ self.wait(8)
self.stop_ambient_camera_rotation()
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 : <a href="https://github.com/architsangal">architsangal</a>
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal)
<br/></br>
## Sub-Topics Covered:
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/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),
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
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file5.gif
Binary files 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
index d4ae50c..1df6413 100644
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif
Binary files differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/README.md b/FSF-2020/linear-algebra/linear-transformations/README.md
index cf81d01..067755e 100644
--- a/FSF-2020/linear-algebra/linear-transformations/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/README.md
@@ -1,5 +1,5 @@
# Contributer: Archit Sangal
-My Github Account : <a href="https://github.com/architsangal">architsangal</a>
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal). These code were written during the course of FOSSEE Summer Fellowship 2020 under the FLOSS: Mathematics using Python.
<br/></br>
## Sub-Topics Covered:
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md
index d21c4dc..6c90bf4 100644
--- a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md
@@ -1,11 +1,11 @@
# Contributer: Archit Sangal
-My Github Account : <a href="https://github.com/architsangal">architsangal</a>
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal)
<br/></br>
## Sub-Topics Covered:
+ The Four Fundamental Subspaces
-#### Video 1: Video 1: Writing System of linear equations in form of Ax=b
+#### Video 1: Writing System of linear equations in form of Ax=b
![GIF1](file11.gif)
#### Video 2: Column Space is same as the image of Linear Transformation
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md
index ee1a337..9d49b4f 100644
--- a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md
@@ -1,5 +1,5 @@
# Contributer: Archit Sangal
-My Github Account : <a href="https://github.com/architsangal">architsangal</a>
+My Github Account : <a href="https://github.com/architsangal">architsangal</a> (https://github.com/architsangal)
<br/></br>
## Sub-Topics Covered:
generated by cgit (git 2.34.1) at 2025-02-10 22:43:20 +0000