Congruence of polynomial matrices

Abstract

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.