Eventually nonnegative matrices are similar to seminonnegative matrices.
type: Item
instance of: scholarly article
title: Eventually nonnegative matrices are similar to seminonnegative matrices.
zbMATH Open document ID: 1052.15017
author: Sarah Carnochan Naqvi
author: J. J. McDonald
published in: Linear Algebra and its Applications
publication date: 2004-05-27T00:00:00Z
review text: Seminonnegative matrices are a subclass of the eventually nonnegative matrices that share many of the combinatorial properties of nonnegative matrices. In Section 3, the authors complete the characterization of the Jordan forms that are similar to eventually nonnegative matrices. In Section 4, they show that if an irreducible seminonnegative matrix is \(m\)-cyclic, then for every positive integer \(g\), \(A^g\) is permutationally similar to the direct sum of \(k\) irreducible matrices where \(k= \text{gcd}(g, m)\).
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 2069730
zbMATH Keywords: Eventually nonnegative matrices
zbMATH Keywords: Jordan form
zbMATH Keywords: Seminonnegative matrices
zbMATH Keywords: Index of cyclicity
zbMATH Keywords: Height characteristic
zbMATH Keywords: Level characteristic
zbMATH Keywords: irreducible matrices
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
full work available at URL: j.laa.2003.11.021
OpenAlex ID: W1989423797
cites work: Q3943082
cites work: The combinatorial structure of eventually nonnegative matrices
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cites work: A characterization of Jordan canonical forms which are similar to eventually nonnegative matrices with the properties of nonnegative matrices.
cites work: On the Jordan form of an irreducible matrix with eventually non-negative powers
DOI: 10.1016/J.LAA.2003.11.021
description: scientific article; zbMATH DE number 2069730