| The semidefinite linear complementarity problem (SDLCP) is a generalization of the linear complementarity problem (LCP) in which linear transformations replace matrices and the cone of positive semidefinite matrices replaces the nonnegative orthant. We study a number of linear transformation classes (some of which are introduced for the first time) and extend several known results in LCP theory to the SDLCPs, and in particular, results which are related to the key properties of uniqueness, feasibility and convexity. Finally, we introduce some new characterizations related to the class of matrices E* and the uniqueness of the LCPs. |
