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) -![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 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) -![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 +![GIF1](file2.gif) \ 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