Solving the Yang-Baxter-like Matrix Equation for a Class of Elementary Matrices
Let u and v be two n-dimensional vectors in the complex field such that v(T)u not equal 0, and let A = I - uv(T). We find all the solutions of the quadratic matrix equation AXA = XAX in various situations, with the help of a spectral perturbation result for rank-one updated matrices. Two numerical examples are given to demonstrate the effectiveness of the method, including an application of the result to a 4 x 4 equation related to the classic Yang-Baxter equation. (C) 2016 Elsevier Ltd. All rights reserved.
Computers and Mathematics with Applications
(2016). Solving the Yang-Baxter-like Matrix Equation for a Class of Elementary Matrices. Computers and Mathematics with Applications, 72(6), 338-343.
Available at: https://aquila.usm.edu/fac_pubs/17834