On an inequality for the Hadamard product of an \(M\)-matrix and its inverse
type: Item
instance of: scholarly article
title: On an inequality for the Hadamard product of an \(M\)-matrix and its inverse
zbMATH Open document ID: 0946.15014
DOI: 10.1016/S0024-3795(99)00224-4
author: Yongzhong Song
published in: Linear Algebra and its Applications
publication date: 2000-10-22T00:00:00Z
review text: Let \(A=[a_{jk}]\) be an \(n\times n\) \(M\)-matrix whose inverse is doubly stochastic. Then \[ q(A\circ A^{-1})\geq 2\max a_{kk}/(n \max a_{kk}-n+1), \] where \(\circ\) denotes the Hadamard product, \(q(B)=1/p(B^{-1})\) and \(p(C)\) is the Perron eigenvalue of a nonnegative matrix \(C\).
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 1419716
zbMATH Keywords: doubly stochastic matrix
zbMATH Keywords: Perron eigenvalue
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: \(M\)-matrix
zbMATH Keywords: inequality
zbMATH Keywords: inverse
zbMATH Keywords: Hadamard product
MaRDI profile type: Publication
cites work: Q3943082
cites work: A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix
cites work: An inequality for the Hadamard product of an M-matrix and an inverse M- matrix
cites work: Matrix Analysis
cites work: On a bound for the Hadamard product of an M-matrix and its inverse
cites work: Q5604166
description: scientific article; zbMATH DE number 1419716