Two inequalities for the Perron root
type: Item
instance of: scholarly article
title: Two inequalities for the Perron root
zbMATH Open document ID: 0618.15010
DOI: 10.1016/0024-3795(87)90220-5
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: If A and B are irreducible, nonnegative \(n\times n\) matrices with a common right and a common left eigenvector corresponding to their respective spectral radii r(A), r(B), then it is shown that \(r(tA+(1- t)B^+)\geq tr(A)+(1-t)r(B)\), where \(0\leq t\leq 1\) and \(B^+\) denotes the transpose of B. Previous inequalities due to \textit{B. W. Levinger} [Notices Am. Math. Soc. 17, 260 (1970)] and \textit{S. Friedland} and \textit{S. Karlin} [Duke II Math. J. 42, 459-490 (1975; Zbl 0373.15008)] are generalized.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4002282
zbMATH Keywords: Perron-Frobenius theory
zbMATH Keywords: irreducible nonnegative matrix
zbMATH Keywords: spectral radius
zbMATH Keywords: eigenvector
author: R. B. Bapat
reviewed by: Dénes Petz
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90220-5
OpenAlex ID: W2005364212
cites work: Applications of an inequality in information theory to matrices
cites work: Some inequalities for the spectral radius of non-negative matrices and applications
cites work: Perron roots of a convex combination of a cone preserving map and its adjoint
cites work: Linear Statistical Inference and its Applications
Wikidata QID: Q126622075
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description: scientific article; zbMATH DE number 4002282