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 mcyoung.xyz
What is a Matrix? A Miserable Pile of Coefficients! ยท mcyoung
| | lisyarus.github.io
Uniqueness of matrix inverses | lisyarus blog
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| | susam.net
Product of Additive Inverses - Susam Pal
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| | [AI summary] This article explains why the product of two negative numbers is positive, using mathematical proofs and ring axioms to generalize the rule beyond basic arithmetic.
| | thenumb.at
Functions are Vectors
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| | [AI summary] The text discusses the representation of functions as vectors and their applications in various domains such as signal processing, geometry, and physics. It explains how functions can be treated as vectors in a vector space, leading to the concept of eigenfunctions and eigenvalues, which are crucial for understanding and manipulating signals and geometries. The text also covers different types of Laplacians, including the standard Laplacian, higher-dimensional Laplacians, and the Laplace-Beltrami operator, and their applications in fields like image compression, computer graphics, and quantum mechanics. The discussion includes spherical harmonics, which are used in representing functions on spheres, and their applications in game engines and glo...
| | dominiczypen.wordpress.com
A Funny Field | Musings on general topology and orderings
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| Let $latex \omega$ denote the first infinite cardinal - that is, the set of non-negative integers. Let $latex p_0 = 2$ be the smallest prime number, and let $latex (p_n)_{n\in\omega}$ enumerate all prime numbers in ascending order. Let $latex \mathcal{U}$ be a free ultrafilter on $latex \omega$. We consider the field $latex F = \big(\prod_{n\in\omega}\mathbb{Z}/p_n\mathbb{Z}\big)/{\mathcal...