Some Rank Formulas for the Yang-Baxter Matrix Equation AXA = XAX Article Swipe

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Rank (graph theory) Matrix (chemical analysis) Mathematics Applied mathematics Algebra over a field Combinatorics Pure mathematics Chemistry Chromatography

Lifang Dai , Maolin Liang , Yonghong Shen ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1051/wujns/2021266459 · OA: W4205179925

Let A be an arbitrary square matrix, then equation AXA =XAX with unknown X is called Yang-Baxter matrix equation. It is difficult to find all the solutions of this equation for any given A . In this paper, the relations between the matrices A and B are established via solving the associated rank optimization problem, where B = AXA = XAX , and some analytical formulas are derived, which may be useful for finding all the solutions and analyzing the structures of the solutions of the above Yang-Baxter matrix equation.