On semigroups of normal matrices
type: Item
instance of: scholarly article
title: On semigroups of normal matrices
zbMATH Open document ID: 1027.15011
DOI: 10.1016/S0024-3795(02)00670-5
author: Bojana Zalar
published in: Linear Algebra and its Applications
publication date: 2003-07-30T00:00:00Z
review text: Semigroups of normal complex square matrices having a finite spectrum are studied. It is shown that every member \(A\) of such a semigroup satisfies the condition \(A^*= A^n\), where \(n\) does not depend on the matrix \(A\). It is shown that such a semigroup is completely reducible and each irreducible contraction consists of a group of unitary matrices and, eventually, the zero matrix. In Section 2 it is concerned with the equivalence between the semigroups having finite spectrum and semigroups of power-Hermitian matrices. In Section 3 it is concerned with the reducibility of semigruops of normal matrices.
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1956800
zbMATH Keywords: normal matrices
zbMATH Keywords: spectrum
zbMATH Keywords: semigroups
zbMATH Keywords: reducibility
zbMATH Keywords: power-Hermitian matrices
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
cites work: Q4061081
cites work: Normal matrices
cites work: Power symmetric stochastic matrices
full work available at URL: s0024-3795(02)00670-5
OpenAlex ID: W1999695041
description: scientific article; zbMATH DE number 1956800