The solution of the matrix polynomial equationA(s)X(s) + B(s)Y(s) = C(s)

This note 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)
have a minimal possible degree. This procedure will result in a unique solution that is obtained by solving a set of linear equations. An example is given to illustrate the procedure.