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

页码：457 / 462

页数：6

共 8 条

[1] [Anonymous], 1991, TOPICS MATRIX ANAL, DOI DOI 10.1017/CBO9780511840371
[2] Spectral radius of Hadamard product versus conventional product for non-negative matrices
Audenaert, Koenraad M. R.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (01) : 366 - 368
[3] Norm inequalities involving Hadamard products
Du, Kun
[J]. LINEAR & MULTILINEAR ALGEBRA, 2010, 58 (02) : 235 - 238
[4] Some inequalities for Hadamard products of matrices
Huang, Rong
[J]. LINEAR & MULTILINEAR ALGEBRA, 2008, 56 (05) : 543 - 554
[5] Mond B., 2000, Electronic Journal of Linear Algebra, V6, P56
[6] Zhan X., 2009, ADV WORKSH TRENDS DE
[7] Zhan X., 2002, LECT NOTES MATH, V1790
[8] Zhang F., 2010, ELECTRON J LINEAR AL, V20, P90, DOI [10.13001/1081-3810.1359, DOI 10.13001/1081-3810.1359]

← 1 →