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www.jeremykun.com | ||
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stephenmalina.com
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| | | | | Selected Exercises # 5.A # 12. Define $ T \in \mathcal L(\mathcal P_4(\mathbf{R})) $ by $$ (Tp)(x) = xp'(x) $$ for all $ x \in \mathbf{R} $. Find all eigenvalues and eigenvectors of $ T $. Observe that, if $ p = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 $, then $$ x p'(x) = a_1 x + 2 a_2 x^2 + 3 a_3 x^3 + 4 a_4 x^4. | |
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lucatrevisan.wordpress.com
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| | | | | The spectral norm of the infinite $latex {d}&fg=000000$-regular tree is $latex {2 \sqrt {d-1}}&fg=000000$. We will see what this means and how to prove it. When talking about the expansion of random graphs, abobut the construction of Ramanujan expanders, as well as about sparsifiers, community detection, and several other problems, the number $latex {2 \sqrt{d-1}}&fg=000000$... | |
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nhigham.com
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| | | | | In linear algebra terms, a correlation matrix is a symmetric positive semidefinite matrix with unit diagonal. In other words, it is a symmetric matrix with ones on the diagonal whose eigenvalues are all nonnegative. The term comes from statistics. If $latex x_1, x_2, \dots, x_n$ are column vectors with $latex m$ elements, each vector containing... | |
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christopher-beckham.github.io
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| | | Techniques for label conditioning in Gaussian denoising diffusion models | ||
