Abstract
The class of matrices Q(0), characterized as all n by n matrices M, for which the linear complementarity problem, y = Mx + q, y greater than or equal to 0, x greater than or equal to 0, y'x = 0 has a solution whenever y = Mx + g, y greater than or equal to 0, x greater than or equal to 0 has a solution, is embedded in a class Q(0) of n by 2n matrices A satisfying: if q is an element of Pos(A) = {Au: u greater than or equal to 0}, then Aw = q has a complementary solution w(t) = (y(t),x(t))greater than or equal to 0 with y(t)x = 0. Here y and x are n-vectors. A characterization of Q(0) is established. As a consequence of this, a new characterization of the matrix class eo as well as some other relevant results are obtained.