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www.depthfirstlearning.com | ||
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peterbloem.nl
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| | | | | [AI summary] The pseudo-inverse is a powerful tool for solving matrix equations, especially when the inverse does not exist. It provides exact solutions when they exist and least squares solutions otherwise. If multiple solutions exist, it selects the one with the smallest norm. The pseudo-inverse can be computed using the singular value decomposition (SVD), which is numerically stable and handles cases where the matrix does not have full column rank. The SVD approach involves computing the SVD of the matrix, inverting the non-zero singular values, and then reconstructing the pseudo-inverse using the modified SVD components. This method is preferred due to its stability and ability to handle noisy data effectively. | |
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francisbach.com
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| | | | | [AI summary] This mathematical post explores the geometry of positive semi-definite matrices using the von Neumann entropy and related Bregman divergences to derive concentration inequalities for random matrices. | |
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pomax.github.io
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| | | | | A detailed explanation of Bézier curves, and how to do the many things that we commonly want to do with them. | |
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dominiczypen.wordpress.com
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| | | Motivation. We show that the space $latex (\aleph_1, \aleph_1\cup\{\aleph_1\})$ satisfies the selection principle $latex {\Omega \choose T}$, but not $latex {\Omega \choose \Gamma}$. This gives a negative answer to the question "$latex {\Omega \choose T} = {\Omega \choose \Gamma}?$" in the general setting. Below is a self-contained treatment of the matter.Let $latex (X,\tau)$ be a... | ||
