A contribution to the theory of M-matrices
type: Item
instance of: scholarly article
title: A contribution to the theory of M-matrices
zbMATH Open document ID: 0696.15016
DOI: 10.1016/0024-3795(89)90006-2
author: Tomasz Szulc
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: Recall that a real \(n\times n\) matrix \(A=(a_{ij})\) with \(a_{ij}\leq 0\) for all \(i\neq j\) is an M-matrix if A is nonsingular and all the elements of \(A^{-1}\) are nonnegative. The author proves that if \(A=(a_{ij})\) is an \(n\times n\) M-matrix with \(a_{ii}>0\) for \(i=1,2,...,n\) then \[ \sum_{1\leq i<j\leq n}\frac{a_{ij}a_{ji}}{a_{ii}a_{jj}}<\frac{n- 1}{2}\quad for\quad n=3,5,7,... \] \[ \sum_{1\leq i<j\leq n}\frac{a_{ij}a_{ji}}{a_{ii}a_{jj}}<\frac{n}{2}\quad for\quad n=2,4,6,...\quad. \]
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 4139946
zbMATH Keywords: M-matrix
reviewed by: Fergus J. Gaines
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90006-2
OpenAlex ID: W2047068626
cites work: Monotonicity of matrices with positive main diagonal
cites work: A lower bound for the Perron root of a nonnegative matrix
cites work: Q5342712
description: scientific article; zbMATH DE number 4139946