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leimao.github.io | ||
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austinmorlan.com
It took me longer than necessary to understand how a rotation transform matrix rotates a vector through three-dimensional space. Not because it's a difficult concept but because it is often poorly explained in textbooks. Even the most explanatory book might derive the matrix for a rotation around one axis (e.g., x) but then present the other two matrices without showing their derivation. I'll explain my own understanding of their derivation in hopes that it will enlighten others that didn't catch on right away. |
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bldavies.com
Let \(A\) be the \(n\times n\) matrix with \({ij}^\text{th}\) entry \(A_{ij}=\min\{i,j\}\). From a previous post, we know \(A\) has a tridiagonal inverse \(A^{-1}\) with \({ij}^\text{th}\) entry1 $$\left[A^{-1}\right]_{ij}=\begin{cases} 2 & \text{if}\ i=j |
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hadrienj.github.io
In this post, we will see special kinds of matrix and vectors the diagonal and symmetric matrices, the unit vector and the concept of orthogonality. |
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thomasvilhena.com
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