Abstract
In this paper we investigate a subclass W of the n × n real matrices. A matrix M belongs to W if and only if certain pairs of its complementary cones intersect only in the zero vector. We show that W ⊆ U , where U is the class of matrices M for which LCP( q, M) (the linear complementarity problem) has a unique solution whenever q belongs in the interior of the union of its complementary cones. Membership in W can be established by solving 2 n-1 systems of linear equations. Finally, several sufficient conditions are given on a matrix in W so that it possesses nonnegative principal minors.
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