Extremal inverse eigenvalue problem for bordered diagonal matrices

被引：30

作者：

Pickmann, Hubert ^{[1
]}

Egana, Juan ^{[1
]}

Soto, Ricardo L. ^{[1
]}

机构：

[1] Univ Catolica Norte, Dept Matemat, Antofagasta, Chile

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2007年 / 427卷 / 2-3期

关键词：

symmetric bordered diagonal matrices; matrix inverse eigenvalue problem;

D O I：

10.1016/j.laa.2007.07.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The following inverse eigenvalue problem was introduced and discussed in [J. Peng, X.Y. Hu, L. Zhang, Two inverse eigenvalue problems for a special kind of matrices, Linear Algebra Appl. 416 (2006) 336347]: to construct a real symmetric bordered diagonal matrix A from the minimal and maximal eigenvalues of all its leading principal submatrices. However, the given formulae in [4, Theorem 11 to compute the matrix A may lead us to a matrix, which does not satisfy the requirements of the problem. In this paper, we rediscuss the problem to give a sufficient condition for the existence of such a matrix and necessary and sufficient conditions for the existence of a nonnegative such a matrix. Results are constructive and generate an algorithmic procedure to construct the matrices. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：256 / 271

页数：16

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