On \(k\)-\(EP\) matrices
type: Item
instance of: scholarly article
title: On \(k\)-\(EP\) matrices
zbMATH Open document ID: 0886.15033
DOI: 10.1016/S0024-3795(97)00066-9
author: J. Ning
published in: Linear Algebra and its Applications
publication date: 1998-01-28T00:00:00Z
review text: Let \(\mathbb{C}_{n\times n}\) be the space of \(n\times n\) complex matrices of order \(n\). A matrix \(A\in \mathbb{C}_{n\times n}\) is an EP matrix if \(N(A)= N(A^*)\), where \(N(A)\) is the null space and \(A^*\) is the conjugate transpose of \(A\) respectively [see \textit{I. J. Katz} and \textit{M. H. Pearl}, J. Res. Natl. Bur. Stand., Sect. B 70, 47-77 (1966; Zbl 0138.01401)]. Let \(k\) be a fixed product of disjoint transformations in \(S_n= \{1,2,\dots, n\}\). A matrix \(A\in \mathbb{C}_{n\times n}\) is \(k\)-Hermitian if \(a_{ij}= \overline{a}_{k(j), k(i)}\) for \(i,j\in \{1,2,\dots,n\}\) [see \textit{R. D. Hill} and \textit{S. R. Waters}, Linear Algebra Appl. 169, 17-29 (1992; Zbl 0757.15011)]. The authors introduce the concept of \(k\)-EP matrices as a generalization of \(k\)-Hermitian and EP matrices. Relations between \(k\)-EP and EP matrices are discussed and necessary and sufficient conditions are determined for a matrix to be \(k\)-EP.
reviewed by: K.Burian
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 1100771
zbMATH Keywords: \(k\)-Hermitian matrix
zbMATH Keywords: \(k\)-EP matrices
MaRDI profile type: Publication
cites work: Theorems on products of \(EP_{r}\) matrices
cites work: Q4061081
cites work: On \(\kappa\)-real and \(\kappa\)-Hermitian matrices
cites work: On EPr and normal Epr matrices
cites work: OnEPrmatrices with entries from an arbitrary field
cites work: On normal and EPr-matrices
cites work: Q3287260
full work available at URL: s0024-3795(97)00066-9
OpenAlex ID: W2007494915
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description: scientific article; zbMATH DE number 1100771