On the parametrization of linearizations of polynomial matrices

In this note we propose a new approach for the construction of a parametrization of the linearizations corresponding to a given polynomial matrix. A linearization of a polynomial matrix is a first order polynomial matrix which is in a certain sense equivalent to the original one. The main advantage of linearization techniques, is that in most cases, a linearization can be easily constructed from the coefficients of the polynomial matrix. In view of their advantages and applications many linearization techniques have been developed by several authors in the recent years. In the present paper we propose a unifying approach aiming to serve as a bridge between the two main linearization approaches already known in the literature.