On the spectral radius and the spectral norm of Hadamard products of nonnegative matrices

被引：12
|
作者：
Huang, Zejun [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 434卷 / 02期
关键词：
Hadamard product; Kronecker product; Nonnegative matrix; Spectral radius; Spectral norm; INEQUALITIES;
D O I：
10.1016/j.laa.2010.08.038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the spectral radius inequality rho(A(1) circle A(2) circle ... circle A(k)) <= rho(A(1)A(2) ... A(k)) for nonnegative matrices using the ideas of Horn and Zhang. We obtain the inequality parallel to A circle B parallel to <= rho(A(T)B) for nonnegative matrices, which improves Schur's classical inequality parallel to A circle B parallel to <= parallel to A parallel to parallel to B parallel to, where parallel to . parallel to denotes the spectral norm. We also give counterexamples to two conjectures about the Hadamard product. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：457 / 462
页数：6
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