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djalil.chafai.net | ||
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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... | |
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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... | |
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pfzhang.wordpress.com
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| | | | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | |
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uncommongenders.home.blog
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| | | [AI summary] The post discusses the creation of a moodboard featuring soft, floral elements and gender-neutral themes, with a focus on aesthetic design and personal expression. | ||
