On products of EP matrices
type: Item
instance of: scholarly article
title: On products of EP matrices
zbMATH Open document ID: 0868.15015
DOI: 10.1016/0024-3795(95)00693-1
author: R. E. Hartwig
author: Irving J. Katz
published in: Linear Algebra and its Applications
publication date: 1997-08-21T00:00:00Z
review text: In this note the authors give necessary and sufficient conditions for a product of two \(n\times n\) complex EP matrices to be EP. All matrices will be complex, and rank, ranges, and row spaces are denoted by \(r(\cdot)\), \(R(\cdot)\), and \(RS(\cdot)\), respectively. A matrix is called EP if \(R(A)= R(A^*)\) and that the group inverse \(A^\sharp\) of \(A\) exists exactly when \(r(A)= r(A^2)\). The main theorem is as follows: THEOREM. Let \(A,B\in C_{n\times n}\) be EP. Then the following are equivalent: i) \(R(AB)= R(A)\cap R(B)\) and \(RS(AB)= RS(A)\cap RS(B)\). ii) \(R(AB)\subset R(B)\) and \(RS(AB)\subset R(A).\) iii) \(AB\) is EP.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 991128
zbMATH Keywords: group matrices
zbMATH Keywords: generalized inverses
zbMATH Keywords: complex \(EP\) matrices
zbMATH Keywords: rank
zbMATH Keywords: ranges
zbMATH Keywords: row spaces
zbMATH Keywords: group inverse
MaRDI profile type: Publication
full work available at URL: 0024-3795(95)00693-1
OpenAlex ID: W2042926054
cites work: Theorems on products of \(EP_{r}\) matrices
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description: scientific article; zbMATH DE number 991128