On the generalized nullspace of M-matrices and Z-matrices
type: Item
instance of: scholarly article
title: On the generalized nullspace of M-matrices and Z-matrices
zbMATH Open document ID: 0647.15005
DOI: 10.1016/0024-3795(88)90019-5
author: Daniel Hershkowitz
author: Hans Schneider
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: A preferred set for a matrix is an ordered set of vectors such that the image of each vector is a nonnegative linear combination of the subsequent ones. The coefficients in the linear combination depend on the graph structure of the matrix. The main goal of the paper is to reprove the preferred basis theorem for the generalized nullspace. The idea is originated from an early paper of the second author [Proc. Edinburgh math. Soc. Ser. 10, 108-122 (1956; Zbl 0074.254)], where the associated graph was supposed to be linearly ordered. The theorem is also extended from M-matrices to Z-matrices.
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 4055783
zbMATH Keywords: M-matrix
zbMATH Keywords: Z-matrix
zbMATH Keywords: Frobenius normal form
zbMATH Keywords: reduced graph
zbMATH Keywords: preferred basis
reviewed by: Dénes Petz
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90019-5
OpenAlex ID: W2137665908
cites work: Characterizations and classifications of M-matrices using generalized nullspaces
cites work: Solutions of Z-matrix equations
cites work: On the singular graph and the Weyl characteristic of an M-matrix
cites work: Algebraic eigenspaces of nonnegative matrices
cites work: Q3239304
cites work: The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: a survey
cites work: On Nonnegative Solutions of Matrix Equations
description: scientific article; zbMATH DE number 4055783