All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two

All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two

Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of t...

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Veröffentlicht in:Complexity (New York, N.Y.) N.Y.), 2020, Vol.2020 (2020), p.1-7
Hauptverfasser: Zhou, Duanmei, Ding, Jiawen
Format: Artikel
Sprache:eng
Schlagworte:
Commuting
Eigenvalues
Numerical analysis
Statistical mechanics
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Zusammenfassung:Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/2585602