Regular matrices in the semigroup of Hall matrices
type: Item
instance of: scholarly article
title: Regular matrices in the semigroup of Hall matrices
zbMATH Open document ID: 0787.05018
DOI: 10.1016/0024-3795(93)90512-M
author: Han Hyuk Cho
published in: Linear Algebra and its Applications
publication date: 1993-12-08T00:00:00Z
review text: Let \(H_ n\) denote the set of all \(n\)-square matrices \(A\) over the Boolean algebra of order two such that \(\text{per}(A)>0\) (semigroup of Hall matrices). Moreover, let, for any positive integer \(s\), \(H_ n(s)= \{A\in H_ n: \text{ per}(A)\geq s\}\). A matrix \(A\in H_ n\) is called regular if there exists a generalized inverse of \(A\) in the same set; \(A\) is called semiinvertible in \(H_ n\) if there exists a semiinverse of \(A\) in the same set. The paper presents a variety of characterizations of regular matrices in \(H_ n\) and \(H_ n(s)\) in terms of idempotent matrices, semiinvertible matrices, adjoint matrices, and identifying permutation matrices.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 459079
zbMATH Keywords: Boolean matrices
zbMATH Keywords: permanents
zbMATH Keywords: Hall matrices
zbMATH Keywords: regular matrices
MaRDI profile type: Publication
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full work available at URL: 0024-3795(93)90512-m
OpenAlex ID: W2015927856
description: scientific article; zbMATH DE number 459079