Bounds for the greatest characteristic root of a nonnegative matrix
type: Item
instance of: scholarly article
title: Bounds for the greatest characteristic root of a nonnegative matrix
zbMATH Open document ID: 0851.15014
DOI: 10.1016/S0024-3795(96)90008-7
published in: Linear Algebra and its Applications
publication date: 1996-11-26T00:00:00Z
review text: A nonnegative matrix of order \(n\) is considered for which two bounds are improved and generalized, namely: \[ \min_i r_i\leq r\leq \max_i r_i \tag{1} \] and \[ \min_i \Biggl( {1\over r_i} \sum^n_{t=1} a_{it} r_t \Biggr)\leq r \leq \max_i \Biggl( {1\over r_i} \sum^n_{t=1} a_{it} r_t \Biggr), \tag{2} \] where \(r_i\), \(i= 1, 2, \dots, n\), are the row sums.to \(A\).
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 881692
zbMATH Keywords: greatest characteristic root
zbMATH Keywords: upper and lower bounds
zbMATH Keywords: nonnegative matrix
author: Shulin Liu
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
cites work: Q5337220
cites work: Bounds for the Greatest Latent Roots of a Positive Matrix
cites work: Bounds for the Greatest Latent Root of a Positive Matrix
cites work: The theorems of Ledermann and Ostrowski on positive matrices
cites work: Bounds for the maximal characteristic root of a non-negative irreducible matrix
cites work: Bounds for the greatest characteristic root of an irreducible nonnegative matrix
cites work: Bounds for the greatest characteristic root of an irreducible nonnegative matrix. II
description: scientific article; zbMATH DE number 881692