Bounds for joint spectral radii of a set of nonnegative matrices
type: Item
instance of: scholarly article
title: Bounds for joint spectral radii of a set of nonnegative matrices
zbMATH Open document ID: 1202.15022
DOI: 10.1134/S0001434610010025
published in: Mathematical Notes
publication date: 2010-09-24T00:00:00Z
review text: For a finite set \(\Sigma\) of nonnegative matrices of order \(n\) the upper and lower joint spectral radius is defined. Bounds for these magnitudes are given in terms of the following matrix \(S=(s_{ij})\), where \(s_{ij} = \max\{\sum_ka_{ik}:A \in \Sigma, a_{ij} >0\}\) and in terms of the similarly defined matrix \(S^-\). It is shown that the upper joint spectral radius is bounded by the max spectral radius of \(S\) and that a similar result holds for the lower joint spectral radius. This generalizes results for the case of one matrix. In the proof methods of max algebra are used.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A80
zbMATH DE Number: 5791014
zbMATH Keywords: max algebra
zbMATH Keywords: upper and lower joint spectral radius
zbMATH Keywords: idempotent semiring
zbMATH Keywords: idempotent algebra
zbMATH Keywords: idempotent semifield
zbMATH Keywords: spectral max-radius
zbMATH Keywords: nonnegative matrices
author: Yury A. Al'pin
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
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full work available at URL: s0001434610010025
OpenAlex ID: W2088643973
description: scientific article; zbMATH DE number 5791014