Extensions of P-property, R0-property and Semidefnite Linear Complementarity Problems

Abstract

In this manuscript, we present some new results for the semidenite linear complementarity problem, in the context of three notions for linear transformations,
viz., pseudo w-P property, pseudo-Jordan w-P property, and pseudo-SSM property. Interconnections with the P#-property (proposed recently in the literature) is presented. We also study the R#-property of a linear transformation, extending the rather well-known notion of an R0-matrix. In particular, results are presented for
the Lyapunov, the Stein and the multiplicative transformations.