Mathematics Faculty Articles

Title

Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefininte matrices

Document Type

Article

Publication Date

2-1-2010

Publication Title

Electronic Journal of Linear Algebra

Keywords

Hadamard product, Nonnegative matrix, Positive semidefinite matrix, Positive definite matrix, Spectral radius, Kronecker product, Matrix inequality

ISSN

1081-3810

Volume

20

First Page

90

Last Page

94

Abstract

X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius

Comments

AMS subject classifications. 15A45, 15A48, 15A69

DOI

10.13001/1081-3810.1359

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