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All Commuting Solutions of a Quadratic Matrix Equation for General Matrices
  
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KeyWord:Jordan canonical form  Sylvester’s equation
Author NameAffiliation
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.