Relations between \(\{ K; s+1\} \)-potent matrices and different classes of complex matrices
type: Item
instance of: scholarly article
title: Relations between \(\{ K; s+1\} \)-potent matrices and different classes of complex matrices
zbMATH Open document ID: 1264.15019
author: Leila Lebtahi
author: Óscar Romero
author: Néstor Thome
published in: Linear Algebra and its Applications
publication date: 2013-03-06T00:00:00Z
review text: The authors consider \(\{ K; s+1 \}\)-potent matrices. A matrix \(A \in \mathbb C^{n \times n}\) is called \(\{ K; s+1 \}\)-potent when \(K\,A^{s+1}\,K = A\) where \(K\) is an involutory matrix and \(s \in \{ 1,2,3,\dots \}\). Specifically, \(\{ K; s+1 \}\)-potent matrices are analyzed considering their relations to different classes of complex matrices; these classes of matrices are: \(\{ s+1 \}\)-generalized projectors, \(\{ K \}\)-Hermitian matrices, normal matrices, and matrices \(B \in \mathbb C^{n \times n}\) (anti-)commuting with \(K\) or such that \(K\,B\) is involutory, Hermitian or normal. In addition, some new relations for \(K\)-generalized centrosymmetric matrices are derived.
reviewed by: Ludwig Kohaupt
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15B10
zbMATH DE Number: 6142071
zbMATH Keywords: involutory matrix
zbMATH Keywords: idempotent matrix
zbMATH Keywords: \(\{ K
zbMATH Keywords: s+1\}\)-potent matrix
zbMATH Keywords: normal matrix
zbMATH Keywords: centrosymmetric matrix
zbMATH Keywords: \(\{ s+1 \}\)-potent matrix
zbMATH Keywords: Hermitian matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2011.10.042
OpenAlex ID: W2051642176
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DOI: 10.1016/J.LAA.2011.10.042
description: scientific article; zbMATH DE number 6142071