Abstract
We study the commuting solutions of the Yang–Baxter matrix equation A X A = X A X when A is an arbitrary square matrix. By characterizing its commuting solutions based on projection matrices, we show that projections can be determined by using the generalized eigenspaces corresponding to the eigenvalues of A . Therefore, commuting solutions can be constructed explicitly. Our results are more general than those obtained recently by Dong (2017), Ding and Zhang (2014), and Ding and Rhee (2013).
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