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| | francisbach.com
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| | nickhar.wordpress.com
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| | 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...
| | matheuscmss.wordpress.com
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| | In 1966, M. Kac wrote a famous article asking whetherCan one hear the shape of drum?: mathematically speaking, one wants to reconstruct (up to isometries) a domain from the knowledge of the spectrum of its Laplacian. In his article, M. Kac showed that one can hear the shape of a disk $latex {\mathbb{D}(0,R)=\{z\in\mathbb{R}^2:|z|\leq R\}}&fg=000000$ because...
| | dismalsci.wordpress.com
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| As an experiment, I have recently started using Vim as my primary text editor. While I have been an Emacs aficionado for a very, very long time - clocking in at almost 16 years - Vim is something that I have always been curious about, and tinkered with from time to time, while ending up...