Matrices with signed generalized inverses
type: Item
instance of: scholarly article
title: Matrices with signed generalized inverses
zbMATH Open document ID: 0967.15002
DOI: 10.1016/S0024-3795(00)00233-0
published in: Linear Algebra and its Applications
publication date: 2001-09-03T00:00:00Z
review text: A complete characterization for \(m\times n\) matrices \(A\) with \(\rho(A)=n\) to have signed generalized inverses is given. The case \(\rho(A) <n \leq m\) is considered and complete characterizations are obtained for \(m \times n\) matrices with \(\rho(A)<n\leq m\) to have signed generalized inverses. The property of having a signed generalized inverse for a matrix \(A\) is inherited by all the submatrices \(B\) of \(A\) with \(\rho(B)= \rho(A)\) and is also inherited by all those matrices \(A_1\) with \(\rho(A_1)= \rho(A)\) which can be obtained from \(A\) by replacing some nonzero entries of \(A\) by zero. A characterization of matrices in a special triangular block form to have signed generalized inverses is also carried out.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 1559344
zbMATH Keywords: signed generalized inverses
zbMATH Keywords: characterizations
author: Jia-Yu Shao
author: Hai-Ying Shan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1559344