A note on singular values of Cauchy-Toeplitz matrices
نویسندگان
چکیده
منابع مشابه
Singular values of convex functions of matrices
Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
متن کاملA note on inversion of Toeplitz matrices
It is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملOn group inverse of singular Toeplitz matrices
In this paper we show that the group inverse of a real singular Toeplitz matrix can be represented as the sum of products of lower and upper triangular Toeplitz matrices. Such a matrix representation generalizes “Gohberg–Semencul formula” in the literature. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A09; 65F20
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We apply the method of determinants to study the distribution of the largest singular values of large real rectangular random matrices with independent Cauchy entries. We show that statistical properties of the largest singular values are different from the Tracy-Widom law. Among other corollaries of our method we show an interesting connection between the mathematical expectations of the deter...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)10016-7