where PA(z) and QA(z) are polynomials in z and PA(z) and QA(z) have no common factor. We define the degree of F(z) to be the maximum degree of PA(Z) for all possible choices of the constant matrix A. The symbol 5F(z) is used to denote the degree of the matrix F(z). The same symbolism is used to denote the degree of a polynomial. With this notation the definition of degree may be expressed by the relation