求解二次矩阵方程秩-3矩阵的交换解

摘要

令A=PQT,其中P和Q是两个n×3的满秩矩阵.当QTP非奇异时,本文给出了二次矩阵方程AXA=XAX的所有交换解.%Let A=PQT, where P and Q are two n×3 complex matrices of full column rank such as QTP is nonsingular.All the commuting solutions of the quadratic matrix equation AXA=XAX are solved completely.