On hidden Z-matrices and the linear complementarity problem

In this paper, we explore various matrix-theoretic aspects of the hidden Z class and demonstrate how the concept of principal pivot transform can be effectively used to extend many existing results. In fact, we revisit various results obtained for hidden Z class by Mangasarian, Cottle and Pang in context of solving linear complementarity problems as linear programs. We identify hidden Z-matrices of special category and discuss the number of solutions of the associated linear complementarity problems. We also present game theoretic interpretation of various results related to hidden Z class and obtain proofs following the game theoretic approach of Raghavan for a subclass of Z-matrices.