Characterizing Q-linear transformations for semidefinite linear complementarity problems

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