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JNMA
JAAC
All Commuting Solutions of a Quadratic Matrix Equation for General Matrices
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KeyWord
:
Jordan canonical form
Sylvester’s equation
Author Name
Affiliation
Qixiang Dong
School of Mathematical Sciences
,
Yangzhou University
,
Yangzhou 225002
,
China
Jiu Ding
School of Mathematics and Natural Sciences
,
University of Southern Mississippi
,
Hattiesburg
,
MS 39406
,
USA
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Abstract
:
Using the Jordan canonical form and the theory of Sylvester’s equation, we find all the commuting solutions of the quadratic matrix equation AXA = XAX for an arbitrary given matrix A.
