An upper bound on the smallest singular value of a square random matrix

Tatarko Kateryna

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An upper bound on the smallest singular value of a square random matrix

机译：平方随机矩阵的最小奇异值的上限

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摘要

Let A = (a(ij)) be a square n x n matrix with i.i.d. zero mean and unit variance entries. It was shown by Rudelson and Vershynin in 2008 that the upper bound for the smallest singular value s(n)(A) is of order n(-1/2) with probability close to one under the additional assumption that the entries of A satisfy Ea(11)(4) infinity. We remove the assumption on the fourth moment and show the upper bound assuming only Ea(11)(2) = 1. (C) 2018 Elsevier Inc. All rights reserved.

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《Journal of complexity》 |2018年第10期|119-128|共10页
作者
Tatarko Kateryna;
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作者单位

Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada;

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原文格式 PDF
正文语种 eng
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关键词
Random matrices; Condition number; Small ball probability; Invertibility of random matrices; Heavy tails; Smallest singular value;

机译：随机矩阵;条件数;小球概率;随机矩阵的可逆性;重尾;最小奇异值;

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An upper bound on the smallest singular value of a square random matrix

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