On a Solution of the Quaternion Matrix Equation X-AXB=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 XAXB=Ccharacterizes the existence of a solution to the matrix equation, and derives closedform 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-AXB=C.