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| | terrytao.wordpress.com
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| | This is yet another post in a series on basic ingredients in the structural theory of locally compact groups, which is closely related to Hilbert's fifth problem. In order to understand the s...
| | mattbaker.blog
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| | I'm teaching Graduate Algebra this semester, and I wanted to record here the proof I gave in class of the (existence part of the) structure theorem for finitely generated modules over a PID. It's a standard argument, based on the existence of the Smith Normal Form for a matrix with entries in a PID, but...
| | qchu.wordpress.com
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| | As an undergraduate the proofs I saw of the Sylow theorems seemed very complicated and I was totally unable to remember them. The goal of this post is to explain proofs of the Sylow theorems which I am actually able to remember, several of which use our old friend The $latex p$-group fixed point theorem...
| | blog.georgeshakan.com
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| Principal Component Analysis (PCA) is a popular technique in machine learning for dimension reduction. It can be derived from Singular Value Decomposition (SVD) which we will discuss in this post. We will cover the math, an example in python, and finally some intuition. The Math SVD asserts that any $latex m \times d$ matrix $latex...