All Commuting Solutions of a Quadratic Matrix Equation for General Matrices

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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 $A$.

Keywords:

Jordan canonical form Sylvester's equation.
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DOI

10.12150/jnma.2020.111

How to Cite

All Commuting Solutions of a Quadratic Matrix Equation for General Matrices. (2024). Journal of Nonlinear Modeling and Analysis, 2(1), 111-123. https://doi.org/10.12150/jnma.2020.111