Let K(M) denote the set of all q „¡ Rn such that the linear complementarity problem LCP(q,M) has a complementary solution. We show that (a) M is an S-matrix iff there is a q0 „¡ K(M) such that q0 < 0 and (b) M is a Q-matrix iff M is a Q0-matrix and an S-m
