Proof of a conjecture of Fiedler and Markham
type: Item
instance of: scholarly article
title: Proof of a conjecture of Fiedler and Markham
zbMATH Open document ID: 0968.15011
DOI: 10.1016/S0024-3795(00)00211-1
published in: Linear Algebra and its Applications
publication date: 2001-09-19T00:00:00Z
review text: Let \(A\) be an \(n\times n\) non-singular \(M\)-matrix and let \(A \circ A^{-1}\) be the Hadamard product of \(A\) and \(A^{-1}\). The author proves that \(q(A\circ A^{-1}) \geq{2\over n}\), where \(q(A\circ A^{-1})\) is the smallest eigenvalue (in modulus) of \(A\circ A^{-1}\). This is an improvement on the lower bound obtained by the author and \textit{Z. Wang} earlier [Linear Algebra Appl. 288, 259-267 (1999; Zbl 0931.15014)]. It also settles the conjecture of \textit{M. Fiedler} and \textit{T. L. Markham} [Linear Algebra Appl. 101, 1-8 (1988; Zbl 0648.15009)].
reviewed by: Harkrishan L. Vasudeva
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1556779
zbMATH Keywords: Hadamard product
zbMATH Keywords: smallest eigenvalue
zbMATH Keywords: lower bound
Wikidata QID: Q123135665
author: Xuerong Yong
MaRDI profile type: Publication
cites work: An inequality for the Hadamard product of an M-matrix and an inverse M- matrix
cites work: On a conjecture of Fiedler and Markham
cites work: On a bound for the Hadamard product of an M-matrix and its inverse
cites work: A Hadamard product involving N-matrices
cites work: Q3943082
cites work: Q4040931
description: scientific article; zbMATH DE number 1556779