Generalization of Mirsky's theorem on diagonals and eigenvalues of matrices

被引：0

作者：

Dokovic, Dragomir Z. ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 437卷 / 10期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Characteristic polynomial; Companion matrix; Principal minors;

D O I：

10.1016/j.laa.2012.06.040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof. Moreover, we show that there is a unique companion-matrix-type solution for this problem. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：2680 / 2682

页数：3

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