From a66349fb0ee9c20eb6dc68b50290cc95424770ea Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Wed, 8 Jul 2020 00:52:56 +0530
Subject: gif added to Linear Transformations
---
...deo 2: Linear Transformation when form 1 is given | Bin 0 -> 50836502 bytes
...atrix Representation Of Linear Transformation.gif | Bin 0 -> 14973890 bytes
...deo 4: Understand Linear Transformations visually | Bin 0 -> 3303032 bytes
.../file13_Video 5: Uniform Scaling | Bin 0 -> 1389092 bytes
...otation by an angle of in anticlockwise direction | Bin 0 -> 9471592 bytes
...y understanding linear transformation(using grid) | Bin 0 -> 19348496 bytes
6 files changed, 0 insertions(+), 0 deletions(-)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid)
(limited to 'FSF-2020/linear-algebra/linear-transformations')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given
new file mode 100644
index 0000000..e9f4b08
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif
new file mode 100644
index 0000000..017e0c7
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually
new file mode 100644
index 0000000..ba6c156
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling
new file mode 100644
index 0000000..fd9bc7b
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction
new file mode 100644
index 0000000..d996130
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid) b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid)
new file mode 100644
index 0000000..683f586
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid) differ
--
cgit
From a651ff753110ac721aa4e7ac47110061b4fa0669 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 02:02:55 +0530
Subject: testing gif updates
---
.../Linear-Transformations-(Linear-Maps)/README.md | 11 ++++++++
...understanding linear transformation(using grid) | Bin 19348496 -> 0 bytes
...understanding_linear_transformation(using_grid) | Bin 0 -> 19348496 bytes
.../file10_Left_Null_Space_pSv8iio_d5Sy9qS.gif | Bin 0 -> 1744023 bytes
.../file10_NOT_in_lecture_note_Column_Space.py | 30 ---------------------
.../file18_NOT_in_lecture_note_Column_Space.py | 30 +++++++++++++++++++++
6 files changed, 41 insertions(+), 30 deletions(-)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_Left_Null_Space_pSv8iio_d5Sy9qS.gif
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_NOT_in_lecture_note_Column_Space.py
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file18_NOT_in_lecture_note_Column_Space.py
(limited to 'FSF-2020/linear-algebra/linear-transformations')
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
new file mode 100644
index 0000000..8ff313b
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/README.md
@@ -0,0 +1,11 @@
+#### Video 1: Visually understanding linear transformation(using grid)
+)
+
+#### Video 2: Linear Transformation when form 1 is given
+
+
+#### Video 3: Matrix Representation Of Linear Transformation
+
+
+#### Divergence of a Remainder
+)
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid) b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid)
deleted file mode 100644
index 683f586..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video 1: Visually understanding linear transformation(using grid) and /dev/null differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid) b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid)
new file mode 100644
index 0000000..683f586
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid) differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_Left_Null_Space_pSv8iio_d5Sy9qS.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_Left_Null_Space_pSv8iio_d5Sy9qS.gif
new file mode 100644
index 0000000..3f50635
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_Left_Null_Space_pSv8iio_d5Sy9qS.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_NOT_in_lecture_note_Column_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_NOT_in_lecture_note_Column_Space.py
deleted file mode 100644
index afe4f9a..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file10_NOT_in_lecture_note_Column_Space.py
+++ /dev/null
@@ -1,30 +0,0 @@
-from manimlib.imports import *
-
-class Column_Space(Scene):
- def construct(self):
-
- A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$")
- A.move_to(2*UP)
- A[1].set_color(color = DARK_BLUE)
- A.scale(0.75)
-
- self.play(Write(A),run_time = 1)
-
- CS_A = TextMobject(r"Column Space of $A = x_{1}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 2 \\ 3 \end{array} \right)$",r"$+x_{2}$",r"$ \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 2 \end{array} \right)$",r"$ + x_{3}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 4 \\ 3 \end{array} \right)$")
- CS_A.move_to(1.5*LEFT+1*DOWN)
- CS_A[1].set_color(color = DARK_BLUE)
- CS_A[3].set_color(color = DARK_BLUE)
- CS_A[5].set_color(color = DARK_BLUE)
- CS_A.scale(0.75)
-
- self.play(Write(CS_A),run_time = 2)
-
- arrow1 = Arrow(start = 1.25*UP,end = 0.25*DOWN+1.75*LEFT)
- arrow2 = Arrow(start = 1.35*UP+0.5*RIGHT,end = 0.25*DOWN+0.5*RIGHT)
- arrow3 = Arrow(start = 1.25*UP+0.75*RIGHT,end = 0.25*DOWN+2.9*RIGHT)
-
- Defn = TextMobject("Linear Combination of Columns of Matrix")
- Defn.move_to(3*DOWN)
-
- self.play(Write(Defn), ShowCreation(arrow1), ShowCreation(arrow2), ShowCreation(arrow3),run_time = 1)
- self.wait(1)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file18_NOT_in_lecture_note_Column_Space.py b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file18_NOT_in_lecture_note_Column_Space.py
new file mode 100644
index 0000000..afe4f9a
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file18_NOT_in_lecture_note_Column_Space.py
@@ -0,0 +1,30 @@
+from manimlib.imports import *
+
+class Column_Space(Scene):
+ def construct(self):
+
+ A = TextMobject(r"$A = $",r"$\left( \begin{array}{c c c} 1 & 2 & 1 \\ 1 & 3 & 1 \\ 2 & 1 & 4 \\ 3 & 2 & 3 \end{array} \right)$")
+ A.move_to(2*UP)
+ A[1].set_color(color = DARK_BLUE)
+ A.scale(0.75)
+
+ self.play(Write(A),run_time = 1)
+
+ CS_A = TextMobject(r"Column Space of $A = x_{1}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 2 \\ 3 \end{array} \right)$",r"$+x_{2}$",r"$ \left( \begin{array}{c} 2 \\ 3 \\ 1 \\ 2 \end{array} \right)$",r"$ + x_{3}$",r"$\left( \begin{array}{c} 1 \\ 1 \\ 4 \\ 3 \end{array} \right)$")
+ CS_A.move_to(1.5*LEFT+1*DOWN)
+ CS_A[1].set_color(color = DARK_BLUE)
+ CS_A[3].set_color(color = DARK_BLUE)
+ CS_A[5].set_color(color = DARK_BLUE)
+ CS_A.scale(0.75)
+
+ self.play(Write(CS_A),run_time = 2)
+
+ arrow1 = Arrow(start = 1.25*UP,end = 0.25*DOWN+1.75*LEFT)
+ arrow2 = Arrow(start = 1.35*UP+0.5*RIGHT,end = 0.25*DOWN+0.5*RIGHT)
+ arrow3 = Arrow(start = 1.25*UP+0.75*RIGHT,end = 0.25*DOWN+2.9*RIGHT)
+
+ Defn = TextMobject("Linear Combination of Columns of Matrix")
+ Defn.move_to(3*DOWN)
+
+ self.play(Write(Defn), ShowCreation(arrow1), ShowCreation(arrow2), ShowCreation(arrow3),run_time = 1)
+ self.wait(1)
\ No newline at end of file
--
cgit
From 591ad26619bda2db76e4256fdf9058e236a75b9d Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 02:05:57 +0530
Subject: testing 2
---
.../Linear-Transformations-(Linear-Maps)/README.md | 2 +-
...y_understanding_linear_transformation(using_grid) | Bin 19348496 -> 0 bytes
...derstanding_linear_transformation(using_grid).gif | Bin 0 -> 19348496 bytes
3 files changed, 1 insertion(+), 1 deletion(-)
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif
(limited to 'FSF-2020/linear-algebra/linear-transformations')
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 8ff313b..a52ccd8 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 @@
#### Video 1: Visually understanding linear transformation(using grid)
-)
+.gif)
#### Video 2: Linear Transformation when form 1 is given
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid) b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid)
deleted file mode 100644
index 683f586..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid) and /dev/null differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif
new file mode 100644
index 0000000..683f586
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif differ
--
cgit
From 23107701f28e4856a359d8c835ef7e396f9bd26e Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 02:08:57 +0530
Subject: testing 3
---
.../Linear-Transformations-(Linear-Maps)/README.md | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
(limited to 'FSF-2020/linear-algebra/linear-transformations')
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 a52ccd8..99a7b62 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 @@
#### Video 1: Visually understanding linear transformation(using grid)
-.gif)
+
#### Video 2: Linear Transformation when form 1 is given
--
cgit
From 600cf20487c45263c71fa15993e4b12b212cceb7 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 02:23:57 +0530
Subject: testing 4
---
.../Linear-Transformations-(Linear-Maps)/README.md | 18 +++++++++++++++---
.../Linear-Transformations-(Linear-Maps)/file10.gif | Bin 0 -> 9471592 bytes
...deo 2: Linear Transformation when form 1 is given | Bin 50836502 -> 0 bytes
.../Linear-Transformations-(Linear-Maps)/file11.gif | Bin 0 -> 50836502 bytes
...atrix Representation Of Linear Transformation.gif | Bin 14973890 -> 0 bytes
.../Linear-Transformations-(Linear-Maps)/file12.gif | Bin 0 -> 19348496 bytes
...deo 4: Understand Linear Transformations visually | Bin 3303032 -> 0 bytes
.../file13_Video 5: Uniform Scaling | Bin 1389092 -> 0 bytes
...otation by an angle of in anticlockwise direction | Bin 9471592 -> 0 bytes
.../Linear-Transformations-(Linear-Maps)/file9.gif | Bin 0 -> 14973890 bytes
...derstanding_linear_transformation(using_grid).gif | Bin 19348496 -> 0 bytes
11 files changed, 15 insertions(+), 3 deletions(-)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10.gif
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9.gif
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif
(limited to 'FSF-2020/linear-algebra/linear-transformations')
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 99a7b62..b266283 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
@@ -1,11 +1,23 @@
#### Video 1: Visually understanding linear transformation(using grid)
-
+
#### Video 2: Linear Transformation when form 1 is given
-
+
#### Video 3: Matrix Representation Of Linear Transformation
-#### Divergence of a Remainder
+#### 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/Linear-Transformations-(Linear-Maps)/file10.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10.gif
new file mode 100644
index 0000000..d996130
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given
deleted file mode 100644
index e9f4b08..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file10_Video 2: Linear Transformation when form 1 is given and /dev/null differ
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
new file mode 100644
index 0000000..e9f4b08
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif
deleted file mode 100644
index 017e0c7..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file11_Video 3: Matrix Representation Of Linear Transformation.gif and /dev/null 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
new file mode 100644
index 0000000..683f586
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually
deleted file mode 100644
index ba6c156..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file12_Video 4: Understand Linear Transformations visually and /dev/null differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling
deleted file mode 100644
index fd9bc7b..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13_Video 5: Uniform Scaling and /dev/null differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction
deleted file mode 100644
index d996130..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14_Video 6: Rotation by an angle of in anticlockwise direction and /dev/null differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9.gif
new file mode 100644
index 0000000..017e0c7
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif
deleted file mode 100644
index 683f586..0000000
Binary files a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file9_Video_1:_Visually_understanding_linear_transformation(using_grid).gif and /dev/null differ
--
cgit
From 6e3b20ca47ec9431302fdd2cd863ad9ca82abfee Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 02:36:40 +0530
Subject: testing 5
---
.../Linear-Transformations-(Linear-Maps)/README.md | 14 +++++++-------
.../Linear-Transformations-(Linear-Maps)/file13.gif | Bin 0 -> 3303032 bytes
.../Linear-Transformations-(Linear-Maps)/file14.gif | Bin 0 -> 1389092 bytes
3 files changed, 7 insertions(+), 7 deletions(-)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14.gif
(limited to 'FSF-2020/linear-algebra/linear-transformations')
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 b266283..8407533 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
@@ -1,23 +1,23 @@
#### 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
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13.gif
new file mode 100644
index 0000000..ba6c156
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file13.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14.gif b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14.gif
new file mode 100644
index 0000000..fd9bc7b
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Linear-Transformations-(Linear-Maps)/file14.gif differ
--
cgit
From a637d8b87fc86f058af30d8855870921b7267b50 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 02:41:33 +0530
Subject: README.md updated with gif(s)
---
.../Linear-Transformations-(Linear-Maps)/README.md | 7 +++++++
FSF-2020/linear-algebra/linear-transformations/README.md | 5 +++--
2 files changed, 10 insertions(+), 2 deletions(-)
(limited to 'FSF-2020/linear-algebra/linear-transformations')
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 8407533..c286736 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
@@ -1,3 +1,10 @@
+# Contributer: Archit Sangal
+My Github Account : architsangal
+
+
+## Sub-Topics Covered:
++ Linear Transformations (Linear Maps)
+
#### Video 1: Visually understanding linear transformation(using grid)
diff --git a/FSF-2020/linear-algebra/linear-transformations/README.md b/FSF-2020/linear-algebra/linear-transformations/README.md
index 692201e..cf81d01 100644
--- a/FSF-2020/linear-algebra/linear-transformations/README.md
+++ b/FSF-2020/linear-algebra/linear-transformations/README.md
@@ -1,9 +1,10 @@
# Contributer: Archit Sangal
My Github Account : architsangal
+
## Sub-Topics Covered:
-+ Vector Space Homomorphisms (Linear Maps)
++ Linear Transformations (Linear Maps)
+ The Four Fundamental Subspaces
+ Rank-Nullity Theorem
+ Orthonormal basis
-+ Gramm-Schmidt Orthogonalization Process
++ Gramm-Schmidt Orthogonalization Process
\ No newline at end of file
--
cgit
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
---
.../file1_introduction.py | 33 --
.../file2_projections.py | 79 -----
.../file3_orthonormal.py | 333 ---------------------
.../file4_Non_Standard_Basis.py | 51 ----
.../README.md | 18 ++
.../file1_introduction.py | 33 ++
.../file2_projections.py | 79 +++++
.../file3_orthonormal.py | 333 +++++++++++++++++++++
.../file4_Non_Standard_Basis.py | 51 ++++
.../file5.gif | Bin 0 -> 26037424 bytes
.../file6.gif | Bin 0 -> 5378916 bytes
.../file7.gif | Bin 0 -> 603223 bytes
.../file8.gif | Bin 0 -> 1027000 bytes
.../Orthonormal Basis/file1_orthogonal.py | 40 ---
.../file2_sum_of_projections_part1.py | 133 --------
.../file3_sum_of_projections_part2.py | 173 -----------
.../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 +++++++++++
.../The-Four-Fundamental-Subspaces/README.md | 30 ++
.../The-Rank-Nullity-Theorem/README.md | 30 ++
22 files changed, 950 insertions(+), 842 deletions(-)
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py
delete mode 100755 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file4_Non_Standard_Basis.py
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file1_introduction.py
create mode 100755 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file2_projections.py
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file5.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file6.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file7.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file8.gif
delete mode 100755 FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
delete mode 100755 FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py
delete mode 100644 FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py
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
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md
(limited to 'FSF-2020/linear-algebra/linear-transformations')
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py
deleted file mode 100644
index ccd23c9..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file1_introduction.py
+++ /dev/null
@@ -1,33 +0,0 @@
-from manimlib.imports import *
-
-class Orthonormal(Scene):
- def construct(self):
- Centre = DOWN
- arrow_1 = Arrow(start = Centre+ORIGIN,end = Centre+1.414*(UP+RIGHT))
- arrow_2 = Arrow(start = Centre+ORIGIN,end = Centre+2*UP)
- arrow_1.scale(1.35)
- arrow_2.scale(1.35)
- text = TextMobject("This is a set of linearly independent vectors")
- text.scale(0.75)
- text.move_to(3*UP+3*LEFT)
- text.set_color(PURPLE_E)
- arrow_1.set_color(PURPLE_E)
- arrow_2.set_color(PURPLE_E)
- self.play(Write(text))
- self.play(ShowCreation(arrow_1), ShowCreation(arrow_2))
- self.wait(2)
- text1 = TextMobject("After we apply Gram-Schmidt Orthogonalization Process to set of linearly independent vectors")
- text1.scale(0.6)
- text1.move_to(3*UP+2*LEFT)
- text1.set_color(GREEN)
- arrow_a = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+RIGHT))
- arrow_a.set_color(GREEN)
- arrow_a.scale(2)
- self.play(Transform(text,text1))
- self.wait(2)
- self.play(Transform(arrow_1,arrow_a))
- arrow_b = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+LEFT))
- arrow_b.set_color(GREEN)
- arrow_b.scale(2)
- self.play(Transform(arrow_2,arrow_b))
- self.wait(2)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py b/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py
deleted file mode 100755
index dd4b8d4..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file2_projections.py
+++ /dev/null
@@ -1,79 +0,0 @@
-from manimlib.imports import *
-
-class Projections(GraphScene):
- CONFIG = {
- "x_min": -6,
- "x_max": 6,
- "y_min": -4,
- "y_max": 4,
- "graph_origin" : ORIGIN ,
- }
- def construct(self):
-
- self.setup_axes(animate=True)
-
- XTD = self.x_axis_width/(self.x_max-self.x_min)
- YTD = self.y_axis_height/(self.y_max-self.y_min)
-
- arrow_a = Arrow(start = ORIGIN, end = 4*XTD*RIGHT)
- arrow_a.scale(1.2)
- arrow_a.set_color(DARK_BLUE)
- arrow_b = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT)
- arrow_b.scale(1.3)
- arrow_b.set_color(DARK_BLUE)
- self.play(ShowCreation(arrow_a), ShowCreation(arrow_b))
-
- text = TextMobject(r"Consider 2 linearly independent vectors $a$ and $b$")
- text.set_color(DARK_BLUE)
- text.scale(0.6)
- text.move_to(3*YTD*UP+5*XTD*LEFT)
- text_a = TextMobject("a")
- text_a.move_to(0.4*YTD*DOWN+3*XTD*RIGHT)
- text_a.set_color(DARK_BLUE)
- text_b = TextMobject("b")
- text_b.move_to(1.5*YTD*UP+RIGHT*XTD)
- text_b.set_color(DARK_BLUE)
-
- self.play(Write(text),Write(text_a), Write(text_b))
- self.wait()
-
- arrow_b_copy = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT)
- arrow_b_copy.scale(1.25)
-
- arrow_p = Arrow(start = ORIGIN, end = 2*XTD*RIGHT)
- arrow_p.scale(1.5)
- arrow_p.set_color(GOLD_E)
-
- text_p = TextMobject("p")
- text_p.move_to(0.25*DOWN+RIGHT)
- text_p.set_color(GOLD_E)
-
- self.play(FadeOut(text), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b))
- text = TextMobject(r"$p$ is the projection of $b$ on $a$")
- text.set_color(GOLD_E)
- text.move_to(3*UP+4*LEFT)
- text.scale(0.8)
- self.play(Write(text),Write(text_p))
- self.wait()
-
- self.play(FadeIn(text_a), FadeIn(text_b))
-
- arrow_o = Arrow(start = 2*XTD*RIGHT, end = 2*YTD*UP+2*XTD*RIGHT)
- arrow_o.scale(1.5)
- arrow_o.set_color(GREEN_E)
-
- text_o = TextMobject("b-p")
- text_o.move_to(UP*YTD+2.7*XTD*RIGHT)
- text_o.set_color(GREEN_E)
-
- self.play(ShowCreation(arrow_o))
- self.play(FadeOut(text),Write(text_o))
-
- text = TextMobject(r"Observe, ($b-p$) is orthogonal to $a$")
- text.set_color(GREEN_E)
- text.move_to(2*DOWN+4*LEFT)
- text.scale(0.8)
- self.play(Write(text))
- self.wait(2)
-
- self.play(FadeOut(self.axes), FadeOut(arrow_a), FadeOut(arrow_b), FadeOut(arrow_b_copy), FadeOut(arrow_o), FadeOut(text_a), FadeOut(text_b), FadeOut(text_o), FadeOut(text_p), FadeOut(text))
\ No newline at end of file
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
deleted file mode 100644
index af51fc6..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file3_orthonormal.py
+++ /dev/null
@@ -1,333 +0,0 @@
-from manimlib.imports import *
-
-class Algo(ThreeDScene):
- def construct(self):
-
- 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.set_color(GREEN)
- text.scale(0.6)
- text.move_to(3*UP+5*LEFT)
- self.play(Write(text))
-
- arrow_a = Arrow(start = ORIGIN, end = 4*RIGHT)
- arrow_a.set_color(GREEN)
- arrow_a.scale(1.15)
- self.play(ShowCreation(arrow_a))
-
- text_a = TextMobject(r"$\beta_1$")
- text_a.move_to(0.4*DOWN+3*RIGHT)
- text_a.set_color(GREEN)
- text_a.scale(0.75)
- self.play(Write(text_a))
- self.wait()
- self.play(FadeOut(text))
-
- text = TextMobject(r"Normalize $\beta_1$ to get $\alpha_1$")
- text.set_color(DARK_BLUE)
- text.scale(0.75)
- text.move_to(3*UP+5*LEFT)
- self.play(Write(text))
-
- alpha_1 = Arrow(start = ORIGIN,end = RIGHT)
- alpha_1.scale(1.9)
- alpha_1.set_color(DARK_BLUE)
- text_alpha_1 = TextMobject(r"$\alpha_1$")
- text_alpha_1.move_to(0.4*DOWN+RIGHT)
- text_alpha_1.set_color(DARK_BLUE)
- text_alpha_1.scale(0.75)
- self.play(Transform(text_a,text_alpha_1), Transform(arrow_a,alpha_1))
- self.wait()
- self.play(FadeOut(text))
-
- 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)
- text.scale(0.6)
- text1.scale(0.6)
- text.move_to(3*UP+4*LEFT)
- text1.move_to(2*UP+4*LEFT)
- self.play(Write(text))
- self.play(Write(text1))
-
- arrow_b = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT)
- arrow_b.scale(1.2)
- arrow_b.set_color(GREEN)
- text_b = TextMobject(r"$\beta_2$")
- text_b.move_to(1.5*UP+RIGHT)
- text_b.set_color(GREEN)
- text_b.scale(0.75)
-
- self.play(ShowCreation(arrow_b), Write(text_b))
- self.wait()
-
- arrow_b_copy = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT)
- arrow_b_copy.scale(1.2)
-
- arrow_p = Arrow(start = ORIGIN, end = 2*RIGHT)
- arrow_p.scale(1.35)
- arrow_p.set_color(GOLD_E)
-
- text_p = TextMobject("p")
- text_p.move_to(0.25*DOWN+RIGHT)
- text_p.set_color(GOLD_E)
-
- self.play(FadeOut(text), FadeOut(text1), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b))
- text = TextMobject(r"$p$ is the projection of $\beta_2$ on $\alpha_1$")
- text.set_color(GOLD_E)
- text.move_to(3*UP+4*LEFT)
- text.scale(0.8)
- self.play(Write(text),Write(text_p))
- self.wait()
-
- self.play(FadeIn(text_b))
-
- arrow_o = Arrow(start = 2*RIGHT, end = 2*UP+2*RIGHT)
- arrow_o.scale(1.35)
- arrow_o.set_color(PURPLE_E)
-
- text_o = TextMobject(r"$\beta_2-p$")
- text_o.move_to(UP+2.7*RIGHT)
- text_o.scale(0.75)
- text_o.set_color(PURPLE_E)
-
- self.play(ShowCreation(arrow_o))
- self.play(FadeOut(text),Write(text_o))
-
- text = TextMobject(r"$\beta_2-p$ is orthogonal to p")
- text1 = TextMobject(r"(and hence orthogonal to $\alpha_1$ also)")
- text.set_color(PURPLE_E)
- text1.set_color(PURPLE_E)
- text.scale(0.7)
- text1.scale(0.7)
- text.move_to(3*UP+4*LEFT)
- text1.move_to(2.5*UP+4*LEFT)
- self.play(Write(text))
- self.play(Write(text1))
- self.wait(2)
-
- self.play(FadeOut(text_p), FadeIn(arrow_a), FadeOut(text), FadeOut(text1), FadeOut(arrow_b_copy), FadeOut(arrow_p), FadeOut(text_b), FadeOut(arrow_b))
- self.play(ApplyMethod(arrow_o.move_to,UP), ApplyMethod(text_o.move_to,RIGHT+UP))
-
- text = TextMobject(r"Now, Normalize $\beta_2-p$")
- text.set_color(DARK_BLUE)
- text.scale(0.6)
- text.move_to(3*UP+4*LEFT)
- self.play(Write(text))
-
- alpha_2 = Arrow(start = ORIGIN,end = UP)
- alpha_2.scale(1.9)
- alpha_2.set_color(DARK_BLUE)
- text_alpha_2 = TextMobject(r"$\alpha_2$")
- text_alpha_2.move_to(0.4*LEFT+UP)
- text_alpha_2.set_color(DARK_BLUE)
- text_alpha_2.scale(0.75)
- self.play(Transform(text_o,text_alpha_2), Transform(arrow_o,alpha_2), FadeIn(text_a))
- self.wait()
- self.play(FadeOut(text),FadeOut(text_a),FadeOut(text_o))
-
- self.add(axes)
- #############################################################################
- axis = TextMobject(r"$\alpha_1$",r"$\alpha_2$",r"$\alpha_3$",r"$\beta_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$")
- axis.scale(0.5)
- axis[0].move_to(0.5*RIGHT+[0,0,-0.5])
- axis[1].move_to(0.5*UP+[0,0,-0.5])
- axis[2].move_to(np.array([0,0,0.5]))
- axis[3].move_to(np.array([1,1,1.5]))
- self.add_fixed_orientation_mobjects(axis[0])
- 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=60*DEGREES,theta=45*DEGREES,run_time=3)
- self.begin_ambient_camera_rotation(rate=0.3)
-
- line1 = Line(start = ORIGIN,end = 1*RIGHT)
- line1.set_color(DARK_BLUE)
- tip1 = Polygon(RIGHT,0.8*RIGHT-0.2*DOWN,0.8*RIGHT-0.2*UP)
- tip1.set_opacity(1)
- tip1.set_fill(DARK_BLUE)
- tip1.set_color(DARK_BLUE)
-
- arrow2 = Line(start = ORIGIN,end = 1*UP)
- arrow2.set_color(DARK_BLUE)
- tip2 = Polygon(UP,0.8*UP-0.2*RIGHT,0.8*UP-0.2*LEFT)
- tip2.set_opacity(1)
- tip2.set_fill(DARK_BLUE)
- tip2.set_color(DARK_BLUE)
- arrow2.set_color(DARK_BLUE)
-
- self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), FadeOut(arrow_a), FadeOut(arrow_o))
- self.wait()
-
- a_line = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2])
- a_line.set_color(GOLD_E)
- a_tip = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8])
- a_tip.set_opacity(1)
- a_tip.set_fill(GOLD_E)
- a_tip.set_color(GOLD_E)
-
- a_line_c1 = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2])
- a_line_c1.set_color(GOLD_E)
- a_tip_c1 = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8])
- a_tip_c1.set_opacity(1)
- 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))
-
- 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)
- self.add_fixed_orientation_mobjects(axis[3])
- text.move_to(3*(DOWN+RIGHT))
- self.play(Write(text))
- self.wait()
- self.play(FadeOut(text))
-
- 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.set_opacity(1)
- p_tip1.set_fill(GOLD_E)
- p_tip1.set_color(GOLD_E)
-
- self.play(Transform(a_line_c1,p_line1),Transform(a_tip_c1,p_tip1))
-
- text = TextMobject(r"Take projection of $\beta_3$ on $\alpha_1$")
- text.scale(0.6)
- text.set_color(GOLD_E)
- self.add_fixed_in_frame_mobjects(text)
- text.move_to(3*(DOWN+RIGHT))
- self.play(Write(text))
- self.wait()
- self.play(FadeOut(text))
-
- o_line1 = Line(start = 2*RIGHT,end = 2*UP+2*RIGHT+[0,0,2])
- o_line1.set_color(GREEN_E)
- o_tip1 = Polygon(2*UP+2*RIGHT+[0,0,2],1.8*UP+2*RIGHT+[0,0,1.8]+0.2*RIGHT,1.8*UP+2*RIGHT+[0,0,1.8]-0.2*RIGHT)
- o_tip1.set_opacity(1)
- o_tip1.set_fill(GREEN_E)
- o_tip1.set_color(GREEN_E)
-
- a_line1 = Line(start = ORIGIN,end = 2*UP+[0,0,2])
- a_line1.set_color(GREEN_E)
- a_tip1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT)
- a_tip1.set_opacity(1)
- a_tip1.set_fill(GREEN_E)
- a_tip1.set_color(GREEN_E)
-
- a_line1_c1 = Line(start = ORIGIN,end = 2*UP+[0,0,2])
- a_line1_c1.set_color(GREEN_E)
- a_tip1_c1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT)
- a_tip1_c1.set_opacity(1)
- a_tip1_c1.set_fill(GREEN_E)
- a_tip1_c1.set_color(GREEN_E)
-
- text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$)")
- text.set_color(GREEN_E)
- text.scale(0.6)
- 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),
- FadeOut(a_line), FadeOut(a_tip), FadeOut(axis[3]),
- Transform(o_line1,a_line1), Transform(o_tip1,a_tip1))
-
- self.wait()
- self.play(FadeOut(text))
-
- p_arrow2 = Line(start = ORIGIN,end = 2*UP)
- p_arrow2.set_color(GOLD_E)
- p_tip2 = Polygon(2*UP,1.8*UP+0.2*RIGHT,1.8*UP+0.2*LEFT)
- p_tip2.set_opacity(1)
- p_tip2.set_fill(GOLD_E)
- p_tip2.set_color(GOLD_E)
- p_arrow2.set_color(GOLD_E)
-
- last_a = Line(start = 2*UP,end = [0,2,2])
- last_a.set_color(PURPLE_E)
- last_a_tip = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT)
- last_a_tip.move_to([0,2,2])
- last_a_tip.set_opacity(1)
- last_a_tip.set_fill(PURPLE_E)
- last_a_tip.set_color(PURPLE_E)
-
- self.wait()
- text = TextMobject(r"Take projection on $\alpha_2$")
- text.scale(0.6)
- text.set_color(GOLD_E)
- self.add_fixed_in_frame_mobjects(text)
- text.move_to(3*(DOWN+RIGHT))
- self.play(Write(text))
- self.play(Transform(a_line1_c1,p_arrow2),Transform(a_tip1_c1,p_tip2))
- self.wait()
- self.play(FadeOut(text))
-
- text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$)")
- text.set_color(PURPLE_E)
- text.scale(0.6)
- 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.wait(2)
- self.play(ShowCreation(last_a_tip), ShowCreation(last_a))
- self.wait()
- self.play(FadeOut(text))
-
- larrow3 = Line(start = ORIGIN,end = [0,0,2])
- larrow3.set_color(PURPLE_E)
- ltip3 = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT)
- ltip3.set_opacity(1)
- ltip3.set_fill(PURPLE_E)
- ltip3.set_color(PURPLE_E)
- self.wait()
- 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 $\alpha_2$")
- text.set_color(PURPLE_E)
- text1.set_color(PURPLE_E)
- text.scale(0.6)
- text1.scale(0.6)
- 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)
- self.play(Write(text))
- self.play(Write(text1))
-
- arrow3 = Line(start = ORIGIN,end = [0,0,1])
- arrow3.set_color(DARK_BLUE)
- 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(DARK_BLUE)
- tip3.set_color(DARK_BLUE)
- self.play(Transform(last_a,arrow3), Transform(last_a_tip,tip3))
- self.add_fixed_orientation_mobjects(axis[2])
-
- self.wait()
- self.play(FadeOut(text),FadeOut(text1))
-
- text = TextMobject(r"These are the three orthonormal vectors $\alpha_1, \alpha_2, \alpha_3$")
- text.set_color(DARK_BLUE)
- self.add_fixed_in_frame_mobjects(text)
- text.scale(0.6)
- text.move_to(3*DOWN+3.5*RIGHT)
- self.play(Write(text))
-
- self.wait(3)
\ No newline at end of file
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
deleted file mode 100644
index 6410a2c..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Gram Schmidt Orthonormalization Process/file4_Non_Standard_Basis.py
+++ /dev/null
@@ -1,51 +0,0 @@
-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)
- tip1.set_opacity(1)
- tip1.set_fill(DARK_BLUE)
- tip1.set_color(DARK_BLUE)
-
- arrow2 = Line(start = ORIGIN,end = 1*UP)
- arrow2.set_color(DARK_BLUE)
- tip2 = Polygon(UP,0.9*UP-0.1*RIGHT,0.9*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([0,0,1],[0,0,0.9]-0.1*RIGHT,[0,0,0.9]-0.1*LEFT)
- tip3.set_opacity(1)
- 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)
-
- 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)
- self.add_fixed_in_frame_mobjects(text)
- text.scale(0.6)
- text.move_to(3*DOWN+3.5*RIGHT)
- self.play(Write(text))
-
- self.wait(7)
\ No newline at end of file
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
new file mode 100644
index 0000000..0305ba7
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/README.md
@@ -0,0 +1,18 @@
+# Contributer: Archit Sangal
+My Github Account : architsangal
+
+
+## Sub-Topics Covered:
++ Gramm-Schmidt Orthogonalization Process
+
+#### Video 1: Introduction to Gram-Schmidt Orthogonalization Process
+
+
+#### Video 2: Obtaining orthogonal vectors using projections
+
+
+#### Video 3: Visual Explanation of how Gram-Schmidt Orthogonalization Process give mutually orthonormal vectors
+
+
+#### Video 4: Example of Orthonormal Vectors which are different from standard basis
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file1_introduction.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file1_introduction.py
new file mode 100644
index 0000000..ccd23c9
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file1_introduction.py
@@ -0,0 +1,33 @@
+from manimlib.imports import *
+
+class Orthonormal(Scene):
+ def construct(self):
+ Centre = DOWN
+ arrow_1 = Arrow(start = Centre+ORIGIN,end = Centre+1.414*(UP+RIGHT))
+ arrow_2 = Arrow(start = Centre+ORIGIN,end = Centre+2*UP)
+ arrow_1.scale(1.35)
+ arrow_2.scale(1.35)
+ text = TextMobject("This is a set of linearly independent vectors")
+ text.scale(0.75)
+ text.move_to(3*UP+3*LEFT)
+ text.set_color(PURPLE_E)
+ arrow_1.set_color(PURPLE_E)
+ arrow_2.set_color(PURPLE_E)
+ self.play(Write(text))
+ self.play(ShowCreation(arrow_1), ShowCreation(arrow_2))
+ self.wait(2)
+ text1 = TextMobject("After we apply Gram-Schmidt Orthogonalization Process to set of linearly independent vectors")
+ text1.scale(0.6)
+ text1.move_to(3*UP+2*LEFT)
+ text1.set_color(GREEN)
+ arrow_a = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+RIGHT))
+ arrow_a.set_color(GREEN)
+ arrow_a.scale(2)
+ self.play(Transform(text,text1))
+ self.wait(2)
+ self.play(Transform(arrow_1,arrow_a))
+ arrow_b = Arrow(start = Centre+ORIGIN,end = Centre+0.707*(UP+LEFT))
+ arrow_b.set_color(GREEN)
+ arrow_b.scale(2)
+ self.play(Transform(arrow_2,arrow_b))
+ self.wait(2)
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file2_projections.py b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file2_projections.py
new file mode 100755
index 0000000..dd4b8d4
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file2_projections.py
@@ -0,0 +1,79 @@
+from manimlib.imports import *
+
+class Projections(GraphScene):
+ CONFIG = {
+ "x_min": -6,
+ "x_max": 6,
+ "y_min": -4,
+ "y_max": 4,
+ "graph_origin" : ORIGIN ,
+ }
+ def construct(self):
+
+ self.setup_axes(animate=True)
+
+ XTD = self.x_axis_width/(self.x_max-self.x_min)
+ YTD = self.y_axis_height/(self.y_max-self.y_min)
+
+ arrow_a = Arrow(start = ORIGIN, end = 4*XTD*RIGHT)
+ arrow_a.scale(1.2)
+ arrow_a.set_color(DARK_BLUE)
+ arrow_b = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT)
+ arrow_b.scale(1.3)
+ arrow_b.set_color(DARK_BLUE)
+ self.play(ShowCreation(arrow_a), ShowCreation(arrow_b))
+
+ text = TextMobject(r"Consider 2 linearly independent vectors $a$ and $b$")
+ text.set_color(DARK_BLUE)
+ text.scale(0.6)
+ text.move_to(3*YTD*UP+5*XTD*LEFT)
+ text_a = TextMobject("a")
+ text_a.move_to(0.4*YTD*DOWN+3*XTD*RIGHT)
+ text_a.set_color(DARK_BLUE)
+ text_b = TextMobject("b")
+ text_b.move_to(1.5*YTD*UP+RIGHT*XTD)
+ text_b.set_color(DARK_BLUE)
+
+ self.play(Write(text),Write(text_a), Write(text_b))
+ self.wait()
+
+ arrow_b_copy = Arrow(start = ORIGIN, end = 2*YTD*UP+2*XTD*RIGHT)
+ arrow_b_copy.scale(1.25)
+
+ arrow_p = Arrow(start = ORIGIN, end = 2*XTD*RIGHT)
+ arrow_p.scale(1.5)
+ arrow_p.set_color(GOLD_E)
+
+ text_p = TextMobject("p")
+ text_p.move_to(0.25*DOWN+RIGHT)
+ text_p.set_color(GOLD_E)
+
+ self.play(FadeOut(text), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b))
+ text = TextMobject(r"$p$ is the projection of $b$ on $a$")
+ text.set_color(GOLD_E)
+ text.move_to(3*UP+4*LEFT)
+ text.scale(0.8)
+ self.play(Write(text),Write(text_p))
+ self.wait()
+
+ self.play(FadeIn(text_a), FadeIn(text_b))
+
+ arrow_o = Arrow(start = 2*XTD*RIGHT, end = 2*YTD*UP+2*XTD*RIGHT)
+ arrow_o.scale(1.5)
+ arrow_o.set_color(GREEN_E)
+
+ text_o = TextMobject("b-p")
+ text_o.move_to(UP*YTD+2.7*XTD*RIGHT)
+ text_o.set_color(GREEN_E)
+
+ self.play(ShowCreation(arrow_o))
+ self.play(FadeOut(text),Write(text_o))
+
+ text = TextMobject(r"Observe, ($b-p$) is orthogonal to $a$")
+ text.set_color(GREEN_E)
+ text.move_to(2*DOWN+4*LEFT)
+ text.scale(0.8)
+ self.play(Write(text))
+ self.wait(2)
+
+ self.play(FadeOut(self.axes), FadeOut(arrow_a), FadeOut(arrow_b), FadeOut(arrow_b_copy), FadeOut(arrow_o), FadeOut(text_a), FadeOut(text_b), FadeOut(text_o), FadeOut(text_p), FadeOut(text))
\ No newline at end of file
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
new file mode 100644
index 0000000..af51fc6
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file3_orthonormal.py
@@ -0,0 +1,333 @@
+from manimlib.imports import *
+
+class Algo(ThreeDScene):
+ def construct(self):
+
+ 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.set_color(GREEN)
+ text.scale(0.6)
+ text.move_to(3*UP+5*LEFT)
+ self.play(Write(text))
+
+ arrow_a = Arrow(start = ORIGIN, end = 4*RIGHT)
+ arrow_a.set_color(GREEN)
+ arrow_a.scale(1.15)
+ self.play(ShowCreation(arrow_a))
+
+ text_a = TextMobject(r"$\beta_1$")
+ text_a.move_to(0.4*DOWN+3*RIGHT)
+ text_a.set_color(GREEN)
+ text_a.scale(0.75)
+ self.play(Write(text_a))
+ self.wait()
+ self.play(FadeOut(text))
+
+ text = TextMobject(r"Normalize $\beta_1$ to get $\alpha_1$")
+ text.set_color(DARK_BLUE)
+ text.scale(0.75)
+ text.move_to(3*UP+5*LEFT)
+ self.play(Write(text))
+
+ alpha_1 = Arrow(start = ORIGIN,end = RIGHT)
+ alpha_1.scale(1.9)
+ alpha_1.set_color(DARK_BLUE)
+ text_alpha_1 = TextMobject(r"$\alpha_1$")
+ text_alpha_1.move_to(0.4*DOWN+RIGHT)
+ text_alpha_1.set_color(DARK_BLUE)
+ text_alpha_1.scale(0.75)
+ self.play(Transform(text_a,text_alpha_1), Transform(arrow_a,alpha_1))
+ self.wait()
+ self.play(FadeOut(text))
+
+ 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)
+ text.scale(0.6)
+ text1.scale(0.6)
+ text.move_to(3*UP+4*LEFT)
+ text1.move_to(2*UP+4*LEFT)
+ self.play(Write(text))
+ self.play(Write(text1))
+
+ arrow_b = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT)
+ arrow_b.scale(1.2)
+ arrow_b.set_color(GREEN)
+ text_b = TextMobject(r"$\beta_2$")
+ text_b.move_to(1.5*UP+RIGHT)
+ text_b.set_color(GREEN)
+ text_b.scale(0.75)
+
+ self.play(ShowCreation(arrow_b), Write(text_b))
+ self.wait()
+
+ arrow_b_copy = Arrow(start = ORIGIN, end = 2*UP+2*RIGHT)
+ arrow_b_copy.scale(1.2)
+
+ arrow_p = Arrow(start = ORIGIN, end = 2*RIGHT)
+ arrow_p.scale(1.35)
+ arrow_p.set_color(GOLD_E)
+
+ text_p = TextMobject("p")
+ text_p.move_to(0.25*DOWN+RIGHT)
+ text_p.set_color(GOLD_E)
+
+ self.play(FadeOut(text), FadeOut(text1), Transform(arrow_b_copy,arrow_p), FadeOut(text_a), FadeOut(text_b))
+ text = TextMobject(r"$p$ is the projection of $\beta_2$ on $\alpha_1$")
+ text.set_color(GOLD_E)
+ text.move_to(3*UP+4*LEFT)
+ text.scale(0.8)
+ self.play(Write(text),Write(text_p))
+ self.wait()
+
+ self.play(FadeIn(text_b))
+
+ arrow_o = Arrow(start = 2*RIGHT, end = 2*UP+2*RIGHT)
+ arrow_o.scale(1.35)
+ arrow_o.set_color(PURPLE_E)
+
+ text_o = TextMobject(r"$\beta_2-p$")
+ text_o.move_to(UP+2.7*RIGHT)
+ text_o.scale(0.75)
+ text_o.set_color(PURPLE_E)
+
+ self.play(ShowCreation(arrow_o))
+ self.play(FadeOut(text),Write(text_o))
+
+ text = TextMobject(r"$\beta_2-p$ is orthogonal to p")
+ text1 = TextMobject(r"(and hence orthogonal to $\alpha_1$ also)")
+ text.set_color(PURPLE_E)
+ text1.set_color(PURPLE_E)
+ text.scale(0.7)
+ text1.scale(0.7)
+ text.move_to(3*UP+4*LEFT)
+ text1.move_to(2.5*UP+4*LEFT)
+ self.play(Write(text))
+ self.play(Write(text1))
+ self.wait(2)
+
+ self.play(FadeOut(text_p), FadeIn(arrow_a), FadeOut(text), FadeOut(text1), FadeOut(arrow_b_copy), FadeOut(arrow_p), FadeOut(text_b), FadeOut(arrow_b))
+ self.play(ApplyMethod(arrow_o.move_to,UP), ApplyMethod(text_o.move_to,RIGHT+UP))
+
+ text = TextMobject(r"Now, Normalize $\beta_2-p$")
+ text.set_color(DARK_BLUE)
+ text.scale(0.6)
+ text.move_to(3*UP+4*LEFT)
+ self.play(Write(text))
+
+ alpha_2 = Arrow(start = ORIGIN,end = UP)
+ alpha_2.scale(1.9)
+ alpha_2.set_color(DARK_BLUE)
+ text_alpha_2 = TextMobject(r"$\alpha_2$")
+ text_alpha_2.move_to(0.4*LEFT+UP)
+ text_alpha_2.set_color(DARK_BLUE)
+ text_alpha_2.scale(0.75)
+ self.play(Transform(text_o,text_alpha_2), Transform(arrow_o,alpha_2), FadeIn(text_a))
+ self.wait()
+ self.play(FadeOut(text),FadeOut(text_a),FadeOut(text_o))
+
+ self.add(axes)
+ #############################################################################
+ axis = TextMobject(r"$\alpha_1$",r"$\alpha_2$",r"$\alpha_3$",r"$\beta_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$",r"$\alpha_3$")
+ axis.scale(0.5)
+ axis[0].move_to(0.5*RIGHT+[0,0,-0.5])
+ axis[1].move_to(0.5*UP+[0,0,-0.5])
+ axis[2].move_to(np.array([0,0,0.5]))
+ axis[3].move_to(np.array([1,1,1.5]))
+ self.add_fixed_orientation_mobjects(axis[0])
+ 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=60*DEGREES,theta=45*DEGREES,run_time=3)
+ self.begin_ambient_camera_rotation(rate=0.3)
+
+ line1 = Line(start = ORIGIN,end = 1*RIGHT)
+ line1.set_color(DARK_BLUE)
+ tip1 = Polygon(RIGHT,0.8*RIGHT-0.2*DOWN,0.8*RIGHT-0.2*UP)
+ tip1.set_opacity(1)
+ tip1.set_fill(DARK_BLUE)
+ tip1.set_color(DARK_BLUE)
+
+ arrow2 = Line(start = ORIGIN,end = 1*UP)
+ arrow2.set_color(DARK_BLUE)
+ tip2 = Polygon(UP,0.8*UP-0.2*RIGHT,0.8*UP-0.2*LEFT)
+ tip2.set_opacity(1)
+ tip2.set_fill(DARK_BLUE)
+ tip2.set_color(DARK_BLUE)
+ arrow2.set_color(DARK_BLUE)
+
+ self.play(ShowCreation(line1), ShowCreation(tip1), ShowCreation(arrow2), ShowCreation(tip2), FadeOut(arrow_a), FadeOut(arrow_o))
+ self.wait()
+
+ a_line = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2])
+ a_line.set_color(GOLD_E)
+ a_tip = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8])
+ a_tip.set_opacity(1)
+ a_tip.set_fill(GOLD_E)
+ a_tip.set_color(GOLD_E)
+
+ a_line_c1 = Line(start = ORIGIN,end = 2*UP+2*RIGHT+[0,0,2])
+ a_line_c1.set_color(GOLD_E)
+ a_tip_c1 = Polygon(2*UP+2*RIGHT+[0,0,2],2*UP+1.6*RIGHT+[0,0,1.8],1.6*UP+2*RIGHT+[0,0,1.8])
+ a_tip_c1.set_opacity(1)
+ 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))
+
+ 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)
+ self.add_fixed_orientation_mobjects(axis[3])
+ text.move_to(3*(DOWN+RIGHT))
+ self.play(Write(text))
+ self.wait()
+ self.play(FadeOut(text))
+
+ 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.set_opacity(1)
+ p_tip1.set_fill(GOLD_E)
+ p_tip1.set_color(GOLD_E)
+
+ self.play(Transform(a_line_c1,p_line1),Transform(a_tip_c1,p_tip1))
+
+ text = TextMobject(r"Take projection of $\beta_3$ on $\alpha_1$")
+ text.scale(0.6)
+ text.set_color(GOLD_E)
+ self.add_fixed_in_frame_mobjects(text)
+ text.move_to(3*(DOWN+RIGHT))
+ self.play(Write(text))
+ self.wait()
+ self.play(FadeOut(text))
+
+ o_line1 = Line(start = 2*RIGHT,end = 2*UP+2*RIGHT+[0,0,2])
+ o_line1.set_color(GREEN_E)
+ o_tip1 = Polygon(2*UP+2*RIGHT+[0,0,2],1.8*UP+2*RIGHT+[0,0,1.8]+0.2*RIGHT,1.8*UP+2*RIGHT+[0,0,1.8]-0.2*RIGHT)
+ o_tip1.set_opacity(1)
+ o_tip1.set_fill(GREEN_E)
+ o_tip1.set_color(GREEN_E)
+
+ a_line1 = Line(start = ORIGIN,end = 2*UP+[0,0,2])
+ a_line1.set_color(GREEN_E)
+ a_tip1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT)
+ a_tip1.set_opacity(1)
+ a_tip1.set_fill(GREEN_E)
+ a_tip1.set_color(GREEN_E)
+
+ a_line1_c1 = Line(start = ORIGIN,end = 2*UP+[0,0,2])
+ a_line1_c1.set_color(GREEN_E)
+ a_tip1_c1 = Polygon(2*UP+[0,0,2],1.8*UP+[0,0,1.8]+0.2*RIGHT,1.8*UP+[0,0,1.8]-0.2*RIGHT)
+ a_tip1_c1.set_opacity(1)
+ a_tip1_c1.set_fill(GREEN_E)
+ a_tip1_c1.set_color(GREEN_E)
+
+ text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$)")
+ text.set_color(GREEN_E)
+ text.scale(0.6)
+ 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),
+ FadeOut(a_line), FadeOut(a_tip), FadeOut(axis[3]),
+ Transform(o_line1,a_line1), Transform(o_tip1,a_tip1))
+
+ self.wait()
+ self.play(FadeOut(text))
+
+ p_arrow2 = Line(start = ORIGIN,end = 2*UP)
+ p_arrow2.set_color(GOLD_E)
+ p_tip2 = Polygon(2*UP,1.8*UP+0.2*RIGHT,1.8*UP+0.2*LEFT)
+ p_tip2.set_opacity(1)
+ p_tip2.set_fill(GOLD_E)
+ p_tip2.set_color(GOLD_E)
+ p_arrow2.set_color(GOLD_E)
+
+ last_a = Line(start = 2*UP,end = [0,2,2])
+ last_a.set_color(PURPLE_E)
+ last_a_tip = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT)
+ last_a_tip.move_to([0,2,2])
+ last_a_tip.set_opacity(1)
+ last_a_tip.set_fill(PURPLE_E)
+ last_a_tip.set_color(PURPLE_E)
+
+ self.wait()
+ text = TextMobject(r"Take projection on $\alpha_2$")
+ text.scale(0.6)
+ text.set_color(GOLD_E)
+ self.add_fixed_in_frame_mobjects(text)
+ text.move_to(3*(DOWN+RIGHT))
+ self.play(Write(text))
+ self.play(Transform(a_line1_c1,p_arrow2),Transform(a_tip1_c1,p_tip2))
+ self.wait()
+ self.play(FadeOut(text))
+
+ text = TextMobject(r"$\beta_3$-(projection of $\beta_3$ on $\alpha_1$ + projection of $\beta_3$ on $\alpha_2$)")
+ text.set_color(PURPLE_E)
+ text.scale(0.6)
+ 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.wait(2)
+ self.play(ShowCreation(last_a_tip), ShowCreation(last_a))
+ self.wait()
+ self.play(FadeOut(text))
+
+ larrow3 = Line(start = ORIGIN,end = [0,0,2])
+ larrow3.set_color(PURPLE_E)
+ ltip3 = Polygon([0,0,2],[0,0,1.8]+0.2*RIGHT,[0,0,1.8]+0.2*LEFT)
+ ltip3.set_opacity(1)
+ ltip3.set_fill(PURPLE_E)
+ ltip3.set_color(PURPLE_E)
+ self.wait()
+ 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 $\alpha_2$")
+ text.set_color(PURPLE_E)
+ text1.set_color(PURPLE_E)
+ text.scale(0.6)
+ text1.scale(0.6)
+ 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)
+ self.play(Write(text))
+ self.play(Write(text1))
+
+ arrow3 = Line(start = ORIGIN,end = [0,0,1])
+ arrow3.set_color(DARK_BLUE)
+ 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(DARK_BLUE)
+ tip3.set_color(DARK_BLUE)
+ self.play(Transform(last_a,arrow3), Transform(last_a_tip,tip3))
+ self.add_fixed_orientation_mobjects(axis[2])
+
+ self.wait()
+ self.play(FadeOut(text),FadeOut(text1))
+
+ text = TextMobject(r"These are the three orthonormal vectors $\alpha_1, \alpha_2, \alpha_3$")
+ text.set_color(DARK_BLUE)
+ self.add_fixed_in_frame_mobjects(text)
+ text.scale(0.6)
+ text.move_to(3*DOWN+3.5*RIGHT)
+ self.play(Write(text))
+
+ self.wait(3)
\ No newline at end of file
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
new file mode 100644
index 0000000..6410a2c
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file4_Non_Standard_Basis.py
@@ -0,0 +1,51 @@
+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)
+ tip1.set_opacity(1)
+ tip1.set_fill(DARK_BLUE)
+ tip1.set_color(DARK_BLUE)
+
+ arrow2 = Line(start = ORIGIN,end = 1*UP)
+ arrow2.set_color(DARK_BLUE)
+ tip2 = Polygon(UP,0.9*UP-0.1*RIGHT,0.9*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([0,0,1],[0,0,0.9]-0.1*RIGHT,[0,0,0.9]-0.1*LEFT)
+ tip3.set_opacity(1)
+ 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)
+
+ 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)
+ self.add_fixed_in_frame_mobjects(text)
+ text.scale(0.6)
+ text.move_to(3*DOWN+3.5*RIGHT)
+ self.play(Write(text))
+
+ self.wait(7)
\ No newline at end of file
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
new file mode 100644
index 0000000..2ce3577
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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
new file mode 100644
index 0000000..7cd7b3d
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diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file7.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file7.gif
new file mode 100644
index 0000000..19a13dd
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diff --git a/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file8.gif b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file8.gif
new file mode 100644
index 0000000..0ef4551
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Gram-Schmidt-Orthonormalization-Process/file8.gif differ
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
deleted file mode 100755
index a5d96f5..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file1_orthogonal.py
+++ /dev/null
@@ -1,40 +0,0 @@
-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
deleted file mode 100755
index 81a0888..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py
+++ /dev/null
@@ -1,133 +0,0 @@
-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
deleted file mode 100644
index 9d25192..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py
+++ /dev/null
@@ -1,173 +0,0 @@
-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
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
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
new file mode 100644
index 0000000..c286736
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/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/The-Rank-Nullity-Theorem/README.md b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/README.md
new file mode 100644
index 0000000..c286736
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/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
--
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')
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
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/Orthonormal-Basis/file6.gif differ
--
cgit
From d55ea3bd90b05ab4ba731d822f347bcdbea67159 Mon Sep 17 00:00:00 2001
From: Archit Sangal
Date: Thu, 9 Jul 2020 03:38:00 +0530
Subject: updated README.md files and gif(s) added
---
.../The-Four-Fundamental-Subspaces/README.md | 34 ++++++++++-----------
.../The-Four-Fundamental-Subspaces/file11.gif | Bin 0 -> 2669469 bytes
.../The-Four-Fundamental-Subspaces/file12.gif | Bin 0 -> 14917563 bytes
.../The-Four-Fundamental-Subspaces/file13.gif | Bin 0 -> 4257387 bytes
.../The-Four-Fundamental-Subspaces/file14.gif | Bin 0 -> 28796385 bytes
.../The-Four-Fundamental-Subspaces/file15.gif | Bin 0 -> 16130920 bytes
.../The-Four-Fundamental-Subspaces/file16.gif | Bin 0 -> 15623398 bytes
.../The-Four-Fundamental-Subspaces/file17.gif | Bin 0 -> 15546537 bytes
.../The-Rank-Nullity-Theorem/README.md | 25 ++-------------
.../The-Rank-Nullity-Theorem/file2.gif | Bin 0 -> 34430418 bytes
10 files changed, 19 insertions(+), 40 deletions(-)
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file11.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file12.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file13.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file14.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file15.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file16.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file17.gif
create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif
(limited to 'FSF-2020/linear-algebra/linear-transformations')
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 c286736..d21c4dc 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
@@ -3,28 +3,28 @@ My Github Account : architsangal
## Sub-Topics Covered:
-+ Linear Transformations (Linear Maps)
++ The Four Fundamental Subspaces
-#### Video 1: Visually understanding linear transformation(using grid)
-
+#### Video 1: Video 1: Writing System of linear equations in form of Ax=b
+
-#### Video 2: Linear Transformation when form 1 is given
-
+#### Video 2: Column Space is same as the image of Linear Transformation
+
-#### Video 3: Matrix Representation Of Linear Transformation
-
+#### Video 3: Existance of Solution w.r.t. vector b
+
-#### Video 4: Understand Linear Transformations visually
-
+#### Video 4: Null Space (Visually)
+
-#### Video 5: Uniform Scaling
-
+#### Video 5: Definition 1 is equivalent to Definition 2
+
-#### Fig.1 Horizontal Shear
-
+#### Video 6: Relation between Row Space and Null Space
+
-#### Fig.2 Vertical Shear
-
+#### Fig. 1 Naming of the left null space
+
-#### Video 6: Rotation by an angle of in anticlockwise direction
-
\ No newline at end of file
+#### Video 7: Left Null Space(Visually)
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file11.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file11.gif
new file mode 100644
index 0000000..8f74202
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file11.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file12.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file12.gif
new file mode 100644
index 0000000..aa7403b
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file12.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file13.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file13.gif
new file mode 100644
index 0000000..34b54c7
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file13.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file14.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file14.gif
new file mode 100644
index 0000000..b77791b
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file14.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file15.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file15.gif
new file mode 100644
index 0000000..8bb24bf
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file15.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file16.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file16.gif
new file mode 100644
index 0000000..87e0026
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file16.gif differ
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file17.gif b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file17.gif
new file mode 100644
index 0000000..eec819a
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/file17.gif differ
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 c286736..ee1a337 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
@@ -3,28 +3,7 @@ My Github Account : architsangal
## Sub-Topics Covered:
-+ Linear Transformations (Linear Maps)
++ The Rank-Nullity Theorem
#### 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
+
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif
new file mode 100644
index 0000000..46efc66
Binary files /dev/null and b/FSF-2020/linear-algebra/linear-transformations/The-Rank-Nullity-Theorem/file2.gif differ
--
cgit