FACTORIZATION OF MATRIX POLYNOMIALS WITH SYMMETRIES

An n x n matrix polynomial L(lambda) (with real or complex coefficient s) is called self-adjoint if L(lambda) = (L(lambdaBAR)) and symmetric if L(lambda) = (L(+/-lambda))T. Factorizations of selfadjoint and symm etric matrix polynomials of the form L(lambda) = (M(lambdaBAR)) DM(lam bda) or L(lambda) = (M(+/-lambda))T DM(lambda) are studied, where D is a constant matrix and M(lambda) is a matrix polynormal. In particular , the minimal possible size of D is described in terms of the elementa ry divisors of L(lambda) and (sometimes) signature of the Hermitian va lues of L(lambda).