On the Yang-Baxter-like matrix equation for rank-two matrices

Abstract

Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.

Keywords

• rank-two matrix
• matrix equation
• jordan form
• 15a18
• 15a24
• 65f15