A lower bound for the Perron root of a nonnegative matrix. II
type: Item
instance of: scholarly article
title: A lower bound for the Perron root of a nonnegative matrix. II
zbMATH Open document ID: 0659.15016
DOI: 10.1016/0024-3795(89)90585-5
author: Tomasz Szulc
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: This paper is a continuation of part I [ibid. 101, 181-186 (1988; reviewed above)]. We obtain a new lower bound for the Perron root r(A) of a nonnegative \(n\times n\) matrix. We show that for A with at least one principal submatrix of order two, with different diagonal entries, and with at least one positive off-diagonal entry, the bound is at least as good as the one in part I, and we determine a class of nonnegative matrices for which it is essentially better. We also show that not every nonnegative square matrix is similar to a nonnegative square matrix with identical diagonal entries.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4077446
zbMATH Keywords: lower bound
zbMATH Keywords: Perron root
zbMATH Keywords: nonnegative matrices
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90585-5
OpenAlex ID: W1970623071
cites work: Bounds for the Perron root of a nonnegative irreducible partitioned matrix
cites work: Nested bounds for the Perron root of a nonnegative matrix
cites work: Bounds for the maximal eigenvalue of a nonnegative irreducible matrix
cites work: Q5331504
cites work: Bounds for the maximal characteristic root of a non-negative irreducible matrix
cites work: A lower bound for the Perron root of a nonnegative matrix
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description: scientific article; zbMATH DE number 4077446