Factorization Problems for Nonmonic Matrix Polynomials

Abstract

In this paper, it is proven that the problem of the nonlinear factorization of a nonmonic matrix polynomial, $L( \lambda ) = L_1 ( \lambda ) L_2 ( \lambda ) \cdots L_k ( \lambda )$, where $L_2 ( \lambda ), \cdots ,L_k ( \lambda )$ are regular, is related to the strict equivalence between two appropriate pencils. These pencils are then obtained from the comonic companion matrices of matrix polynomials $M ( \lambda ),M_1 ( \lambda ), \cdots ,M_k ( \lambda )$ associated with $L( \lambda ),L_1 ( \lambda ), \cdots ,L_k ( \lambda )$.