Commuting Solutions of a Quadratic Matrix Equation for Nilpotent Matrices

被引：11

作者：

Dong, Qixiang ^{[1
]}

Ding, Jiu ^{[2
]}

Huang, Qianglian ^{[3
]}

机构：

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

[2] Univ Southern Mississippi, Dept Math, Hattiesburg, MS 39406 USA

[3] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2018年 / 25卷 / 01期

基金：

中国国家自然科学基金;

关键词：

quadratic matrix equation; nilpotent matrix; Jordan canonical form; Toeplitz matrix; commuting solution;

D O I：

10.1142/S1005386718000032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We solve the quadratic matrix equation AXA = XAX with a given nilpotent matrix A, to find all commuting solutions. We first provide a key lemma, and consider the special case that A has only one Jordan block to motivate the idea for the general case. Our main result gives the structure of all the commuting solutions of the equation with an arbitrary nilpotent matrix.

引用

页码：31 / 44

页数：14

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