Irreducible semigroups of matrices with eigenvalue one
type: Item
instance of: scholarly article
title: Irreducible semigroups of matrices with eigenvalue one
zbMATH Open document ID: 1053.15010
author: J. Bernik
author: M. Omladič
author: H. Radjavi
author: Roman Drnovšek
author: T. Košir
published in: Semigroup Forum
publication date: 2004-03-07T00:00:00Z
review text: The authors study complex \(n\times n\) matrix groups and semigroups with the property that each matrix acting on \(\mathbb C^n\) has a fixed point, or, equivalently has an eigenvalue one. It is shown that for \(4\neq n\geq 3\) there are irreducible matrix groups and irreducible semigroups of nonnegative matrices with this property. In particular, for \(n=3\), the structure of any such semigroup is determined. The authors also present additional hypotheses that imply reducibility.
reviewed by: Huang Wenxue
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 2051545
zbMATH Keywords: fixed points
zbMATH Keywords: groups of matrices
zbMATH Keywords: irreducibility
zbMATH Keywords: matrices with eigenvalue one
zbMATH Keywords: nonnegative matrices
zbMATH Keywords: reducibility
zbMATH Keywords: semigroups of matrices
zbMATH Keywords: symmetric powers of matrices
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2051545