On a bound for the Hadamard product of an M-matrix and its inverse
type: Item
instance of: scholarly article
title: On a bound for the Hadamard product of an M-matrix and its inverse
zbMATH Open document ID: 0726.15011
DOI: 10.1016/0024-3795(91)90069-9
author: Ching Li
author: Ji-Cheng Chen
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: For an \(n\times n\) nonsingular \(M-matrix\) A, let \(q(A\circ A^{-1})\) denote the smallest real eigenvalue of the Hadamard product of A with its inverse \(A^{-1}\). For \(n>2\), it is shown that \(q(A\circ A^{-1})>2/n\) and in fact the inequality is sharp. If \(n=2\), then \(q(A\circ A^{- 1})=1\). This proves a conjecture of \textit{M. Fiedler} and \textit{T. L. Markham} [ibid. 101, 1-8 (1988; Zbl 0648.15009)].
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 4198206
zbMATH Keywords: lower bound of smallest real eigenvalue
zbMATH Keywords: Hadamard product
reviewed by: Ali-Akbar Jafarian
MaRDI profile type: Publication
full work available at URL: 0024-3795(91)90069-9
OpenAlex ID: W2060358315
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: A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
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description: scientific article; zbMATH DE number 4198206