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All solutions of the Yang-Baxter-like matrix equation for nilpotent matrices of index two. (English) Zbl 1441.15013

Summary: 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.

MSC:

15A24 Matrix equations and identities
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