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gpfault.net | ||
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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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ianwrightsite.wordpress.com
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| | | | | Riemann's Zeta function is an infinite sublation of Hegelian integers. | |
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mzucker.github.io
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| | | | | Automatically deriving area elements for various parameterizations of the unit sphere. | |
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djalil.chafai.net
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| | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | ||
