Linearizations of polynomial matrices with symmetries and their applications

In an earlier paper by the present authors, a new family of companion forms associated with a regular polynomial matrix was presented, generalizing similar results by M. Fiedler whoconsidered the scalar case. This family of companion forms preserves both the finite and infiniteelementary divisor structure of the original polynomial matrix, thus all its members can be seen aslinearizations of the corresponding polynomial matrix. In this note, its applications on polynomialmatrices with symmetries, which appear in a number of engineering fields, are examined.