Localization of Perron roots
type: Item
instance of: scholarly article
title: Localization of Perron roots
zbMATH Open document ID: 1067.15004
published in: Linear Algebra and its Applications
publication date: 2004-11-26T00:00:00Z
review text: The localization of the Perron root of a nonnegative irreducible matrix is discussed. Recall the spectral radius of a complex matrix \(A\) is defined as the maximum of absolute values of its eigenvalues. It is known that if a real matrix is irreducible and nonnegative then its spectral radius is its eigenvalue (the Perron root). A new localization method giving relationship between the Perron root of a nonnegative matrix and the estimates of the row sums of its generalized Perron complements is given. Some numerical examples are presented.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 2119131
zbMATH Keywords: Nonnegative irreducible matrix
zbMATH Keywords: Perron complement
zbMATH Keywords: Perron root
zbMATH Keywords: Spectral radius
zbMATH Keywords: eigenvalue
zbMATH Keywords: numerical examples
author: Linzhang Lu
author: Michael Ng
reviewed by: Witold Więsław
MaRDI profile type: Publication
full work available at URL: j.laa.2004.06.016
OpenAlex ID: W1965420532
cites work: Perron eigenvector of the Tsetlin matrix
cites work: Q4326384
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cites work: Inverses of Perron complements of inverse \(M\)-matrices
DOI: 10.1016/J.LAA.2004.06.016
description: scientific article; zbMATH DE number 2119131