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djalil.chafai.net | ||
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nhigham.com
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| | | | | The trace of an $latex n\times n$ matrix is the sum of its diagonal elements: $latex \mathrm{trace}(A) = \sum_{i=1}^n a_{ii}$. The trace is linear, that is, $latex \mathrm{trace}(A+B) = \mathrm{trace}(A) + \mathrm{trace}(B)$, and $latex \mathrm{trace}(A) = \mathrm{trace}(A^T)$. A key fact is that the trace is also the sum of the eigenvalues. The proof is by... | |
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nhigham.com
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| | | | | The spectral radius $latex \rho(A)$ of a square matrix $latex A\in\mathbb{C}^{n\times n}$ is the largest absolute value of any eigenvalue of $LATEX A$: $latex \notag \rho(A) = \max\{\, |\lambda|: \lambda~ \mbox{is an eigenvalue of}~ A\,\}. $ For Hermitian matrices (or more generally normal matrices, those satisfying $LATEX AA^* = A^*A$) the spectral radius is just... | |
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jhui.github.io
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| | | | | Deep learning | |
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blog.computationalcomplexity.org
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| | | In my post about the myth that Logicians are crazy I mentioned in passing that Whitehead and Russell spend 300 pages proving 1+1=2 (but we... | ||
