On Some Properties of the Minimal-in-Degree Irreducible Factorizations of a Rational Matrix

The definition of irreducible factorizations of minimal degree of a rational matrix and a brief description of an algorithm for constructing them are presented. Two properties of such factorizations are established. First, for every proper rational matrix, these factorizations are just its minimal matrix fractiondescriptions (MFDs), and, second, they make it possible to reduce the problem of determining the pole-zero structure of a rational matrix at infinity to that of finding the indices of two polynomial matrices at the zero point. Bibliography: 4 titles.