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mihai.page | ||
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mcyoung.xyz
[AI summary] This text provides an in-depth explanation of linear algebra concepts, including vector spaces, linear transformations, matrix multiplication, and field extensions. It emphasizes the importance of understanding these concepts through the lens of linear maps and their composition, which naturally leads to the matrix multiplication formula. The text also touches on the distinction between vector spaces and abelian groups, and discusses the concept of field extensions, such as [R:Q] and [C:R]. The author mentions their art blog and acknowledges their own drawing of the content. |
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www.scijournal.org
This guide will show you how to write a dot product in LaTeX |
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leanprover-community.github.io
[AI summary] A technical documentation entry for the Lean mathematical library detailing definitions and operations for semimodules, modules, matrices, linear maps, and bilinear forms |
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djalil.chafai.net
This post is devoted to certain properties of random permutation matrices. Let \( {\mathfrak{S}_n} \) be the symmetric group, \( {n\geq2} \), and let \( {\mathcal{P}_n} \) be the group of \( {n\times n} \) permutation matrices, obtained by the isomorphism \( {\sigma\in\mathfrak{S}_n\mapsto P_\sigma={(\mathbf{1}_{j=\sigma(i)})}_{1\leq i,j\leq n}} \). We know that \( {\mathcal{P}_n} \) is a subgroup of the orthogonal group... |
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