On a Solution of the Quaternion Matrix Equation X - A X ~ B = C and Its Application

This paper first studies the solution of a complex matrix equation X - AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation X - A X ~ B = C characterizes the existence of a solution to the matrix equation, and derives closed-form solutions of the matrix equation in explicit forms by means of real representations of quaternion matrices. This paper also gives an application to the complex matrix equation X - A X [macr] B = C .