On strongly degenerate complementary cones and solution rays

In this paper we show that ifA is a matrix in the class of matricesE(d), for ad R ⁿ ,d > 0, introduced by Garcia, then the boundary of the set ofq R ⁿ for which the linear complementarity problem (q, A) has a solution is equal to the union of all strongly degenerate cones of (I, -A). This is a generalization of a similar result for copositive plus matrices observed by Cottle. We also study some related questions.On leave from Indian Statistical Service, Government of India.