document: Relationship between strong monotonicity property , P/sub 2 / - property , and the GUS-property in semidefinite linear complementarity problems In a recent paper on semidefinite linear complementarity problems , Gowda and Song -LRB- 2000 -RRB- introduced and studied the P-property , P/sub 2 / - property , GUS-property , and strong monotonicity property for linear transformation L : S/sup n / to S/sup n / , where S/sup n / is the space of all symmetric and real n * n matrices . In an attempt to characterize the P/sub 2 / - property , they raised the following two questions : -LRB- i -RRB- Does the strong monotonicity imply the P/sub 2 / - property ? -LRB- ii -RRB- Does the GUS-property imply the P/sub 2 / - property ? In this paper , we show that the strong monotonicity property implies the P/sub 2 / - property for any linear transformation and describe an equivalence between these two properties for Lyapunov and other transformations . We show by means of an example that the GUS-property need not imply the P/sub 2 / - property , even for Lyapunov transformations
doc_bio_tags: O O B I I O O O O O O O O O O O B I I I O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O B I I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I
extractive_keyphrases: semidefinite linear complementarity problems strong monotonicity property linear transformation lyapunov transformations
abstractive_keyphrases: p/sub 2/-property gus-property symmetric real matrices