Solving the Yang-Baxter-Like Matrix Equation for Nilpotent Matrices of Index Three
Let A be a nilpotent matrix of index three and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a simplified matrix equation of the same type with A replaced by its Jordan form, whose Jordan blocks are at most 3×3. Then we obtain a system of matrix equations of smaller sizes to find all the commuting solutions of the original matrix equation.
International Journal of Computing Mathematics
(2017). Solving the Yang-Baxter-Like Matrix Equation for Nilpotent Matrices of Index Three. International Journal of Computing Mathematics, 95(2), 303-315.
Available at: https://aquila.usm.edu/fac_pubs/15773