Optimization of the spectral radius of a product for nonnegative matrices
type: Item
instance of: scholarly article
title: Optimization of the spectral radius of a product for nonnegative matrices
zbMATH Open document ID: 1163.15007
author: Lixing Han
author: Daniel Hershkowitz
author: M. Neumann
author: Nung-Sing Sze
author: Jonathan D. Axtell
published in: Linear Algebra and its Applications
publication date: 2009-02-25T00:00:00Z
review text: For an \(n\times n\) irreducible nonnegative matrix \(A\), the authors show that over the set of all \(n\times n\) doubly stochastic matrices \(S\), the multiplicative spectral radius \(\rho (SA)\) attains a minimum and a maximum at a permutation matrix. When \(A\) is symmetric, they prove that \(\rho (S_1A)\geq \rho (S_2A)\), when \(S_1\) and \(S_2\) are two symmetric matrices such that both \(S_1A\) and \(S_2A\) are nonnegative matrices and \(S_1-S_2\) is a positive semidefinite matrix. Some consequences are considered.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5518761
zbMATH Keywords: irreducible nonnegative matrix
zbMATH Keywords: multiplicative spectral radius
zbMATH Keywords: doubly stochastic matrix
reviewed by: C. M.da Fonseca
MaRDI profile type: Publication
full work available at URL: j.laa.2007.05.025
OpenAlex ID: W1995341206
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DOI: 10.1016/J.LAA.2007.05.025
description: scientific article; zbMATH DE number 5518761