Quasicomplete factorizations of rational matrix functions

It is shown that within the class ofn×n rational matrix functions which are analytic at infinity with valueW()=I_n, any rational matrix functionW is the productW=W₁...W_p of rational matrix functionsW₁,...,W_p of McMillan degree one. Furthermore, such a factorization can be established with a number of factors not exceeding 2(W)–1, where (W) denotes the McMillan degree ofW.