Title

Commuting Solutions of a Quadratic Matrix Equation for Nilpotent Matrices

Document Type

Article

Publication Date

3-1-2018

Department

Mathematics

Abstract

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.

Publication Title

Algebra Colloquium

Volume

25

Issue

1

First Page

31

Last Page

44

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