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 --- .../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 +++++++++++++++++++++ 3 files changed, 30 insertions(+), 30 deletions(-) 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/The-Four-Fundamental-Subspaces') 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 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 --- .../The-Four-Fundamental-Subspaces/README.md | 30 ++++++++++++++++++++++ 1 file changed, 30 insertions(+) create mode 100644 FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces/README.md (limited to 'FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces') 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) +![GIF1](file12.gif) + +#### Video 2: Linear Transformation when form 1 is given +![GIF2](file11.gif) + +#### Video 3: Matrix Representation Of Linear Transformation +![GIF3](file9.gif) + +#### Video 4: Understand Linear Transformations visually +![GIF4](file13.gif) + +#### Video 5: Uniform Scaling +![GIF5](file14.gif) + +#### Fig.1 Horizontal Shear +![GIF6](file6_Horizontal_Shear_gif.gif) + +#### Fig.2 Vertical Shear +![GIF7](file7_Vertical_Shear_gif.gif) + +#### Video 6: Rotation by an angle of in anticlockwise direction +![GIF8](file10.gif) \ No newline at end of file -- 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 8 files changed, 17 insertions(+), 17 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 (limited to 'FSF-2020/linear-algebra/linear-transformations/The-Four-Fundamental-Subspaces') 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) -![GIF1](file12.gif) +#### Video 1: Video 1: Writing System of linear equations in form of Ax=b +![GIF1](file11.gif) -#### Video 2: Linear Transformation when form 1 is given -![GIF2](file11.gif) +#### Video 2: Column Space is same as the image of Linear Transformation +![GIF2](file14.gif) -#### Video 3: Matrix Representation Of Linear Transformation -![GIF3](file9.gif) +#### Video 3: Existance of Solution w.r.t. vector b +![GIF3](file17.gif) -#### Video 4: Understand Linear Transformations visually -![GIF4](file13.gif) +#### Video 4: Null Space (Visually) +![GIF4](file12.gif) -#### Video 5: Uniform Scaling -![GIF5](file14.gif) +#### Video 5: Definition 1 is equivalent to Definition 2 +![GIF5](file13.gif) -#### Fig.1 Horizontal Shear -![GIF6](file6_Horizontal_Shear_gif.gif) +#### Video 6: Relation between Row Space and Null Space +![GIF6](file16.gif) -#### Fig.2 Vertical Shear -![GIF7](file7_Vertical_Shear_gif.gif) +#### Fig. 1 Naming of the left null space +![GIF7](file10_Left_Null_Space_pSv8iio_d5Sy9qS.gif) -#### Video 6: Rotation by an angle of in anticlockwise direction -![GIF8](file10.gif) \ No newline at end of file +#### Video 7: Left Null Space(Visually) +![GIF8](file15.gif) \ 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 -- cgit