Some non-commuting solutions of the Yang-Baxter-like matrix equation

Abstract

Let A be a square matrix satisfying A4=A{A}^{4}=A. We solve the Yang-Baxter-like matrix equation AXA=XAXAXA=XAX to find some solutions, based on analysis of the characteristic polynomial of A and its eigenvalues. We divide the problem into small cases so that we can find the solution easily. Finally, in order to illustrate the results, two numerical examples are presented.

Keywords

• diagonalizable matrix
• matrix equation
• jordan form
• eigenvalue
• 15a24