On inverse M-matrices
type: Item
instance of: scholarly article
title: On inverse M-matrices
zbMATH Open document ID: 0673.15007
DOI: 10.1016/0024-3795(89)90574-0
author: Mordechai Lewin
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The author gives necessary and/or sufficient conditions for nonnegative square matrices to be inverse M-matrices, i.e. matrices of the form \(M=sI-B\) where \(B\geq 0\), \(\rho\) (B) is the spectral radius of B and \(s>\rho (B)\). Special cases where the matrices in consideration are also investigated; a square matrix A falls into the first category if \(A_ 1=PAP^ T\) is triangular for some permutation matrix P, and into the second if \(A=I+\alpha C\) where C is a (0,1)-matrix with zero main diagonal. The graph G(A) associated with the matrix A plays a key role in the author's investigations.
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4101377
zbMATH Keywords: graph of a matrix
zbMATH Keywords: essentially triangular matrices
zbMATH Keywords: alpha-matrices
zbMATH Keywords: inverse M-matrices
zbMATH Keywords: (0,1)-matrix
reviewed by: László Mihályffy
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90574-0
OpenAlex ID: W2053101023
cites work: Topological proofs for certain theorems on matrices with non-negative elements
cites work: Notes on inverse M-matrices
cites work: Inverse M-matrices
cites work: Matrices with a transitive graph and inverse M-matrices
cites work: On the inverse M-matrix problem for (0,1)-matrices
cites work: Nonnegative Matrices whose Inverses are M-Matrices
cites work: The inverse M-matrix problem
description: scientific article; zbMATH DE number 4101377