Structure of \({\mathcal H}\)-classes in the semigroup of nonnegative matrices
type: Item
instance of: scholarly article
title: Structure of \({\mathcal H}\)-classes in the semigroup of nonnegative matrices
zbMATH Open document ID: 0542.15005
DOI: 10.1016/0024-3795(84)90073-9
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: This paper inestigates the structure of the \({\mathcal H}\)-classes in the semigroup \(N_ n\) of nonnegative matrices: The main results are as follows. (1). Two sets of equivalent conditions for any two matrices A and B to satisfy A\({\mathcal H}B\) in \(N_ n\) are obtained. (2) A one-to-one and onto correspondence between the \({\mathcal H}\)-class \({\mathcal H}_ A\) and the group \(W_{A_ 0}\) of the greatest cone-independent submatrix \(A_ 0\) of A is established. (3) \(W_{A_ 0}\) can be made up from the groups of the connective submatrices of \(A_ 0\).
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A12
zbMATH DE Number: 3861343
zbMATH Keywords: semigroup of nonnegative matrices
zbMATH Keywords: greatest cone-independent submatrix
zbMATH Keywords: connective submatrices
author: Shangjun Yang
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90073-9
OpenAlex ID: W2072659499
cites work: Q3943082
cites work: A geometric treatment of generalized inverses and semigroups of nonnegative matrices
cites work: Q3848243
cites work: Q4141184
description: scientific article; zbMATH DE number 3861343