Extensions of $P$-Property, $R_0$-Property and Semidefinite Linear Complementarity Problems

I. Jeyaraman, Kavita Bisht, K.C. Sivakumar

In this manuscript, we present some new results for the semidefinite 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) are presented. We also study the $R_#$-property of a linear transformation, extending the rather well known notion of an $R_0$-matrix. In particular, results are presented for the Lyapunov, Stein, and the multiplicative transformations.