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
Recommended Citation
Dong, Q.,
Ding, J.,
Huang, Q.
(2018). Commuting Solutions of a Quadratic Matrix Equation for Nilpotent Matrices. Algebra Colloquium, 25(1), 31-44.
Available at: https://aquila.usm.edu/fac_pubs/15774