Ela a New Family of Companion Forms of Polynomial Matrices

In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. Furthermore, for the special class of self-adjoint polynomial matrices a particular member is shown to be self-adjoint itself. 1. Preliminaries. We consider polynomial matrices of the form (1.1) T (s) = T 0 s n + T 1 s n−1 + ... + T n , with T i ∈ C p×p. A polynomial matrix T (s) is said to be regular iff det T (s) = 0 for almost every s ∈ C. The associated with T (s) matrix pencil