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djalil.chafai.net | ||
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nickhar.wordpress.com
1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... |
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francisbach.com
[AI summary] This technical blog post explores the mathematical properties of symmetric positive definite matrices, specifically focusing on the Löwner order, matrix monotonicity, and matrix convexity in the context of machine learning and optimization. |
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mycqstate.wordpress.com
Today I'd like to sketch a question that's been pushing me in a lot of different directions over the past few years --- some sane, others less so; few fruitful, but all instructive. The question is motivated by the problem of placing upper bounds on the amount of entanglement needed to play a two-player non-local... |
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fabricebaudoin.blog
Exercise 1.Solve Exercise 44 in Chapter 1 of the book. Exercise 2.Solve Exercise 3 in Chapter 1 of the book. Exercise 3.Solve Exercise 39 in Chapter 1 of the book. Exercise 4.The heat kernel on $latex \mathbb{S}^1$ is given by $latex p(t,y) =\frac{1}{2\pi}\sum_{m \in \mathbb{Z}} e^{-m^2 t} e^{im y} =\frac{1}{\sqrt{4\pi t}} \sum_{k \in \mathbb{Z}} e^{-\frac{(y... |
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