  In this paper we establish some applications of the Scherer-Hol's theorem for
polynomial matrices. Firstly, we give a representation for polynomial matrices
positive definite on subsets of compact polyhedra. Then we establish a
Putinar-Vasilescu Positivstellensatz for homogeneous and non-homogeneous
polynomial matrices. Next we propose a matrix version of the
P\'olya-Putinar-Vasilescu Positivstellensatz. Finally, we approximate positive
semi-definite polynomial matrices using sums of squares.
