On the nonsingularity of matrices with certain sign patterns
type: Item
instance of: scholarly article
title: On the nonsingularity of matrices with certain sign patterns
zbMATH Open document ID: 0892.15006
DOI: 10.1016/S0024-3795(97)00341-8
author: Chuanxiang Ji
author: P. N. Shivakumar
published in: Linear Algebra and its Applications
publication date: 1998-03-17T00:00:00Z
review text: The authors propose a nonsingularity criterion for matrices \(A= (a_{ij})_{m \times m}\) of the following two types of sign distribution: \[ \text{SD1: for }i\leq j,\;a_{ij}>0; \text{ for } i>j,\;(-1)^{i+j} a_{ij}>0; \] \[ \text{SD2: for } i\leq j,\;a_{ij} >0; \text{ for } i>j,\;(-1)^{i+j+1} a_{ij} >0 \] to be sign-nonsingular. Such matrices arise in the solution of linear systems for Poisson's equation in doubly connected regions by using difference equations or finite element methods. The criterion consists of a set of conditions which is easily computable and sufficient. A numerical example is given for demonstrating the theory.
reviewed by: Yang Yingchen
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1129379
zbMATH Keywords: nonsingularity of matrices
zbMATH Keywords: sign nonsingular
zbMATH Keywords: sign distribution
zbMATH Keywords: numerical example
MaRDI profile type: Publication
cites work: Strong forms of nonsingularity
cites work: A note concerning positive matrices and M-Matrices
cites work: Q5340130
cites work: Viscous flow in pipes whose cross-sections are doubly connected regions
cites work: When the sign pattern of a square matrix determines uniquely the sign pattern of its inverse
cites work: Q4358012
full work available at URL: s0024-3795(97)00341-8
OpenAlex ID: W2038275711
description: scientific article; zbMATH DE number 1129379