In the setting of semidenite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X);:=X-AXA^T$, and show that $S_A$ is (strictly) monotone if and only if ${ u}_r(UAU^T{circ};UAU^T)$(<)${leq}1$, for all orthogonal matrices U where ${circ}$ is the Hadamard product and ${ u}_r$ is the real numerical radius. In particular, we show that if ${ ho}(A)$ < 1 and ${ u}_r(UAU^T{circ};UAU^T){leq}1$, then SDLCP($S_A$, Q) has a unique solution for all $Q{in}S^n$. In an attempt to characterize the GUS-property of a nonmonotone $S_A$, we give an instance of a nonnormal $2{ imes}2$ matrix A such that SDLCP($S_A$, Q) has a unique solution for Q either a diagonal or a symmetric positive or negative semidenite matrix. We show that this particular $S_A$ has the $P^{prime}_2$-property.