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 × 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.