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nhigham.com | ||
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djalil.chafai.net
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| | | | | Let $X$ be an $n\times n$ complex matrix. The eigenvalues $\lambda_1(X), \ldots, \lambda_n(X)$ of $X$ are the roots in $\mathbb{C}$ of its characteristic polynomial. We label them in such a way that $\displaystyle |\lambda_1(X)|\geq\cdots\geq|\lambda_n(X)|$ with growing phases. The spectral radius of $X$ is $\rho(X):=|\lambda_1(X)|$. The singular values $\displaystyle s_1(X)\geq\cdots\geq s_n(X)$ of $X$ are the eigenvalues of the positive semi-definite Hermitian... | |
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nla-group.org
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| | | | | by Sven Hammarling and Nick Higham It is often thought that Jim Wilkinson developed backward error analysis because of his early involvement in solving systems of linear equations. In his 1970 Turing lecture [5] he described an experience, during world war II at the Armament Research Department, of solving a system of twelve linear equations | |
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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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francisbach.com
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