Congruence of polynomial matrices

Let R = C[t] be the ring of all polynomials in the real variable t with complex coefficients. We show that if A is an n-square hermitian matrix with entries in R, then A is congruent to the direct sum of a zero matrix and a diagonally dominant matrix. Here, diagonally dominant means that the degree of any main diagonal entry is greater than the degree of any other entry in the same row and column. (C) 1999 Elsevier Science Inc. All rights reserved.