From b3194a1bef5062ed1304c7e68811656a1ce9f4ed Mon Sep 17 00:00:00 2001 From: Karan Jayachandra Date: Mon, 20 Apr 2026 08:52:33 +0200 Subject: Added the image to explain linear and affine transforms --- content/posts/linear_algebra/matrices.ipe | 446 ++++++++++++++++++++++++++++++ 1 file changed, 446 insertions(+) create mode 100644 content/posts/linear_algebra/matrices.ipe (limited to 'content/posts/linear_algebra/matrices.ipe') diff --git a/content/posts/linear_algebra/matrices.ipe b/content/posts/linear_algebra/matrices.ipe new file mode 100644 index 0000000..a8a48c4 --- /dev/null +++ b/content/posts/linear_algebra/matrices.ipe @@ -0,0 +1,446 @@ + + + + +\usepackage{amsmath} + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h + + + + + +-0.5 -0.5 m +0.5 -0.5 l +0.5 0.5 l +-0.5 0.5 l +h + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + + + +-0.43 -0.57 m +0.57 0.43 l +0.43 0.57 l +-0.57 -0.43 l +h + + +-0.43 0.57 m +0.57 -0.43 l +0.43 -0.57 l +-0.57 0.43 l +h + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.3 0 l +-0.5 -0.333 l +h + + + + +0.5 0 m +-0.5 0.333 l +-0.3 0 l +-0.5 -0.333 l +h + + + + +1 0 m +0 0.333 l +0 -0.333 l +h +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +1 0 m +0 0.333 l +0 -0.333 l +h +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +176 720 m +176 800 l +256 800 l +256 720 l +h + + +16 720 m +48 784 l +96 784 l +96 736 l +16 720 l + + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{x}_1 +\bf{x}_2 +\bf{x} + +80 736 m +104 800 l + + +80 736 m +136 764 l + +\bf{r}_2 +\bf{r}_1 + +16 720 m +84 804 l + +\bf{y} = \bf{A} \bf{x} + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{r}_1 +\bf{r}_2 +\bf{y} = \begin{bmatrix} +\bf{r}_1 \cdot \bf{x}\\ +\bf{r}_2 \cdot \bf{x} +\end{bmatrix} + +40 784 m +96 784 l + + +96 784 m +96 736 l + + +128 720 m +176 768 l + + +112 752 m +160 752 l + + +176 720 m +176 800 l +256 800 l +256 720 l +h + + +176 720 m +176 800 l +256 800 l +256 720 l +h + +\bf{b} + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{r}_1 +\bf{r}_2 +\bf{y} = \begin{bmatrix} +\bf{r}_1 \cdot \bf{x}\\ +\bf{r}_2 \cdot \bf{x} +\end{bmatrix} + +128 720 m +176 768 l + + +80 736 m +80 816 l + + +80 736 m +160 736 l + +\bf{r}_1 +\bf{r}_2 + +272 720 m +272 720 l +288 752 l + +\bf{z} = \bf{y} + \bf{b} + +112 752 m +160 752 l + + +128 720 m +176 768 l + +\bf{z} + + -- cgit v1.3.1