The Solution of the Matrix Polynomial Equation: A(s)X(s) + B(s)Y(S) = C(s)

This paper presents an algorithm for finding the solution {X(s), Y(s)} of the matrix polynomial equation A(s)X(s) + B(s) Y(s) = C(S). Since the solution, when it exists, is not unique we will find the solution for which the rows of X(s) has a minimal possible degree. This procedure will result in a unique solution which is obtained by solving a set of linear equations. An example is given to illustrate the procedure.