Proof of a conjecture of Fiedler and Markham

被引：20

作者：

Yong, XR ^{[1
]}

机构：

[1] Xinjiang Univ, Dept Math, Urumqi 830046, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 320卷 / 1-3期

关键词：

M-matrix; eigenvalues; Hadamard product; stochastic matrix;

D O I：

10.1016/S0024-3795(00)00211-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be an n x n nonsingular M-matrix. For the Hadamard product A circle A(-1), M. Fiedler and T.L. Markham conjectured in [Linear Algebra Appl. 101 (1988) 1] that q(A circle A(-1)) greater than or equal to 2/n, where q(A circle A(-1)) is the smallest eigenvalue (in modulus) of A circle A(-1). We considered this conjecture in [Linear Algebra Appl. 288 (1999) 259] having observed an incorrect proof in [Linear Algebra Appl. 144 (1991) 171] and obtained that q(A circle A(-1)) greater than or equal to (2/n)(n - 1)/n. The present paper gives a proof for this conjecture, (C) 2000 Elsevier Science Inc. All rights reserved.

引用

页码：167 / 171

页数：5