Sign pattern matrices and generalized inverses
type: Item
instance of: scholarly article
title: Sign pattern matrices and generalized inverses
zbMATH Open document ID: 0811.15005
DOI: 10.1016/0024-3795(94)90082-5
author: Carolyn A. Eschenbach
author: Frank J. Hall
author: Zhongshan Li
published in: Linear Algebra and its Applications
publication date: 1994-12-01T00:00:00Z
review text: A sign pattern matrix is a matrix whose entries consist of element from the set \(\{+,-,0\}\). If \(A\) is a sign pattern matrix, then \(Q(A)\) denotes the set of all real \(n \times n\) matrices \(B\) such that the signs of the entries in \(B\) match the corresponding entries in \(A\). The class \({\mathcal G}\) of all square patterns \(A\) for which there exist \(B,C \in Q(A)\) where \(BCB=B\) is investigated. The main result is that, for nonnegative patterns, \({\mathcal G}\) coincides with the class of all square patterns \(A\) for which there exists a \(B \in Q(A)\) with \(B^ 3 = B\).
reviewed by: Giacomo Bonanno
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 698658
zbMATH Keywords: generalized inverse
zbMATH Keywords: sign pattern matrix
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90082-5
OpenAlex ID: W1969876711
cites work: Q4061081
cites work: Inverses of nonnegative matrices
cites work: Q4002435
cites work: Idempotence for sign-pattern matrices
cites work: Q4281322
cites work: Q5590111
cites work: Q5849795
cites work: Q5645536
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description: scientific article; zbMATH DE number 698658