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nhigham.com | ||
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stephenmalina.com
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| | | | | Matrix Potpourri # As part of reviewing Linear Algebra for my Machine Learning class, I've noticed there's a bunch of matrix terminology that I didn't encounter during my proof-based self-study of LA from Linear Algebra Done Right. This post is mostly intended to consolidate my own understanding and to act as a reference to future me, but if it also helps others in a similar position, that's even better! | |
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tiao.io
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| | | | | Suppose we're given a positive semidefinite (PSD) matrix $\mathbf{A} \in \mathbb{R}^{N \times N}$ to which we wish to update by some low-rank matrix $\mathbf{U} \mathbf{U}^\top \in \mathbb{R}^{N \times N}$, $$\mathbf{B} \triangleq \mathbf{A} + \mathbf{U} \mathbf{U}^\top,$$ where the update factor matrix $\mathbf{U} \in \mathbb{R}^{N \times M}$. To be more precise, the low-rank update is rank-$M$ for some $M \ll N$. What is the best way to calculate the Cholesky decomposition of $\mathbf{B}$? Given ...... | |
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hadrienj.github.io
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| | | | | This post will introduce you to special kind of matrices: the identity matrix and the inverse matrix. We will use Python/Numpy as a tool to get a better intu... | |
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statisticaloddsandends.wordpress.com
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| | | If $latex Z_1, \dots, Z_n$ are independent $latex \text{Cauchy}(0, 1)$ variables and $latex w= (w_1, \dots, w_n)$ is a random vector independent of the $latex Z_i$'s with $latex w_i \geq 0$ for all $latex i$ and $latex w_1 + \dots w_n = 0$, it is well-known that $latex \displaystyle\sum_{i=1}^n w_i Z_i$ also has a $latex... | ||
