Theoretical analysis demonstrates necessary conditions for invertible matrices in Yang–Baxter-like equations, suggesting deeper matrix properties.
Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang–Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang–Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results.
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Wen et al. (2026) studied this question.
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