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
收藏
页码：2680 / 2682
页数：3
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