  In this paper we give a matrix version of Handelman's Positivstellensatz [1],
representing polynomial matrices which are positive definite on convex, compact
polyhedra. Moreover, we propose also a procedure to find such a representation.
As a corollary of Handelman's theorem, we give a special case of Schm\"udgen's
Positivstellensatz for polynomial matrices positive definite on convex, compact
polyhedra.
