On the number of solutions to a class of linear complementarity problems

In this note, we consider the linear complementarity problemw = Mz + q, w 0, z 0, w^Tz = 0, when all principal minors ofM are negative. We show that for such a problem for anyq, there are either 0, 1, 2, or 3 solutions. Also, a set of sufficiency conditions for uniqueness is stated.The work of both authors is partially supported by a grant from the National Science Foundation, MCS 77-03472.