Nonnegative matrices, zero patterns, and spectral inequalities
type: Item
instance of: scholarly article
title: Nonnegative matrices, zero patterns, and spectral inequalities
zbMATH Open document ID: 0687.15013
DOI: 10.1016/0024-3795(89)90380-7
author: Ludwig Elsner
author: Charles R. Johnson
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The theme is inequalities for the spectral radius (\(\rho)\) of a positive linear combination of nonnegative matrices. Here are two of the results. Theorem 3.1: \(\rho (A+sgn(A))\geq \rho (A)+sgn(\rho (A)),\) where sgn is the signum function, applied to a matrix elementwise. Theorem 2.1: Let \(A_ i\) be irreducible and \(t_ i\geq 0\) for \(i=1,...,p\). Let \(P_ i\) be the projector of \(A_ i\) corresponding to its Perron-Frobenius eigenvalue \(\rho (A_ i)\). If \(P_ i-P_ j\) has 0 diagonal for all i and j, then \(\rho (\Sigma t_ iA_ i)\geq \Sigma t_ i\rho (A_ i).\) This theorem has a partial corollary.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4125587
zbMATH Keywords: spectral inequality
zbMATH Keywords: spectral radius
zbMATH Keywords: nonnegative matrices
zbMATH Keywords: irreducible
zbMATH Keywords: Perron-Frobenius eigenvalue
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90380-7
OpenAlex ID: W2017833461
cites work: Two inequalities for the Perron root
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cites work: Some inequalities for the spectral radius of non-negative matrices and applications
cites work: Q3254327
cites work: Symmetric matrices associated with a nonnegative matrix
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description: scientific article; zbMATH DE number 4125587