On Positive Semidefinite Preserving Stein Transformation

초록

In the setting of semidefinite linear complementarity problems on $\text{sn}$,we focus on the Stein Transformation $S_A(X):=X-AX{A}^T$ for $A\in \text{Rnn}$ that is positive semidefinite preserving (i.e., $S_A({\text{sn}}_{+})\subseteq {\text{sn}}_{+}$) and show that such transformation is strictly monotone if and only if it is nondegenerate. We also show that a positive semidefinite preserving $S_A$ has the Ultra-GUS property if and only if $1\notin \sigma (A)\sigma (A).$

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