Bézout and Hankel matrices associated with row reduced matrix polynomials, Barnett-type formulas

Based on the approach introduced by B.D.O. Anderson and E.I. Jury in 1976, the definition of finite Hankel and Bézout matrices corresponding to matrix polynomials is extended to the case where the denominator of the corresponding rational matrix function is not necessarily monic but is row reduced. The matrices introduced keep most of the well-known properties that hold in the monic case. In particular, we derive extensions of formulas giving a connection with polynomials in the companion matrix (usually called Barnett formulas), of the inversion theorem and of formulas concerning alternating products of Hankel and Bézout matrices.