In the setting of semidenite linear complementarity problems on

, we focus on the Stein Transformation

, and show that

is (strictly) monotone if and only if

(<)

, for all orthogonal matrices U where

is the Hadamard product and

is the real numerical radius. In particular, we show that if

< 1 and

, then SDLCP(

, Q) has a unique solution for all

. In an attempt to characterize the GUS-property of a nonmonotone

, we give an instance of a nonnormal

matrix A such that SDLCP(

, Q) has a unique solution for Q either a diagonal or a symmetric positive or negative semidenite matrix. We show that this particular

has the

-property.