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.