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www.ethanepperly.com | ||
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stephenmalina.com
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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francisbach.com
[AI summary] The blog post discusses the spectral properties of kernel matrices, focusing on the analysis of eigenvalues and their estimation using tools like the matrix Bernstein inequality. It also covers the estimation of the number of integer vectors with a given L1 norm and the relationship between these counts and combinatorial structures. The post includes a detailed derivation of bounds for the difference between true and estimated eigenvalues, highlighting the role of the degrees of freedom and the impact of regularization in kernel methods. Additionally, it touches on the importance of spectral analysis in machine learning and its applications in various domains. |
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nhigham.com
The spectral radius $latex \rho(A)$ of a square matrix $latex A\in\mathbb{C}^{n\times n}$ is the largest absolute value of any eigenvalue of $LATEX A$: $latex \notag \rho(A) = \max\{\, |\lambda|: \lambda~ \mbox{is an eigenvalue of}~ A\,\}. $ For Hermitian matrices (or more generally normal matrices, those satisfying $LATEX AA^* = A^*A$) the spectral radius is just... |
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www.jeremykun.com
In our last primer we saw the Fourier series, which flushed out the notion that a periodic function can be represented as an infinite series of sines and cosines. While this is fine and dandy, and quite a powerful tool, it does not suffice for the real world. In the real world, very little is truly periodic, especially since human measurements can only record a finite period of time. Even things we wish to explore on this blog are hardly periodic (for instance, image analysis). |
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