Characterizations of \(\{K,s+1\}\)-potent matrices and applications
type: Item
instance of: scholarly article
title: Characterizations of \(\{K,s+1\}\)-potent matrices and applications
zbMATH Open document ID: 1232.15003
author: Leila Lebtahi
author: Óscar Romero
author: Néstor Thome
published in: Linear Algebra and its Applications
publication date: 2011-12-08T00:00:00Z
review text: The authors introduce a new kind of matrices called \(\{ K, s+1\}\)-potent as an extension of generalized inverse matrices and involutory matrix, which is the generalization of the well-known idempotent matrix. Then they show that for each positive integer \(n\) there exists at least one \(n \times n\) size matrix that belongs to this class and they also present a method to construct an infinite number of \(\{K, s+1\}\)-potent matrices from only one of them. Moreover, they study sums, products, direct sums and inverse of \(\{K, s+1\}\)-potent matrices. Furthermore, the authors present the characterization of \(\{K, s+1\}\)-potent matrices from a spectral point of view, in terms of powers of the matrix, by means of the group inverse, and via block representation of a matrix of index 1. Then they give conditions under which a linear combination of two commuting \(\{K, s+1\}\)-potent matrices is \(\{K, s+1\}\)-potent.
reviewed by: Süleyman Güler
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 5987840
zbMATH Keywords: involutory matrix
zbMATH Keywords: idempotent matrix
zbMATH Keywords: spectrum
zbMATH Keywords: group inverse matrix
zbMATH Keywords: generalized inverse matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2010.11.034
OpenAlex ID: W44608350
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DOI: 10.1016/J.LAA.2010.11.034
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description: scientific article; zbMATH DE number 5987840