On the and P2-properties in the semidefinite linear complementarity problem

Motivated by the so-called P2-property in the semidefinite linear complementarity problems, in this article, we introduce the concept of -property for a linear transformation on the space of real n×n symmetric matrices. While these two properties turn out to be different, we show that they are equivalent for the Lyapunov transformation LA, double-sided multiplicative transformation MA and a particular class of Stein transformations. We also show that implies the SSM and Q-properties.