Characterizing Q-linear transformations for semidefinite linear complementarity problems

Abstract

In this paper we introduce a new class, called F, of linear transformations defined from the space of real n x n symmetric matrices into itself. Within this new class, we show the equivalence between Q- and Q(b)-transformations. We also provide conditions under which a linear transformation belongs to F. Moreover, this class, when specialized to square matrices of size n, turns out to be the largest class of matrices for which such equivalence holds true in the context of standard linear complementary problems.