Category: mathematics |
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jaydaigle.net
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This week we continue our exploration of what numbers are, and where mathematicians keep finding weird ones. Last time we defined the real numbers, but it took a lot of work. Now we'll see how truly strange they are. They're so strange that it's tempting to avoid them and stick with something simpler. But the real numbers do a much better job of describing modeling the parts of the world we care about. Their weirdness is exactly what we need to guarantee that a bunch of
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mcyoung.xyz
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[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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lisyarus.github.io
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[AI summary] The author explores the mathematical challenges of differentiating quaternions, particularly in the context of inverse kinematics, and derives new rules based on central simple algebras.
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