caa a22 4500 47576966X CHVBK 20180406123616.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/PL00011387 doi (NATIONALLICENCE)springer-10.1007/PL00011387 On semidefinite linear complementarity problems [Elektronische Daten] [M. Seetharama Gowda, Yoon Song] Abstract. : Given a linear transformation L:? n →? n and a matrix Q∈? n , where ? n is the space of all symmetric real n×n matrices, we consider the semidefinite linear complementarity problem SDLCP(L,? n +,Q) over the cone ? n + of symmetric n×n positive semidefinite matrices. For such problems, we introduce the P-property and its variants, Q- and GUS-properties. For a matrix A∈R n×n , we consider the linear transformation L A :? n →? n defined by L A (X):=AX+XA T and show that the P- and Q-properties for L A are equivalent to A being positive stable, i.e., real parts of eigenvalues of A are positive. As a special case of this equivalence, we deduce a theorem of Lyapunov. Springer-Verlag Berlin Heidelberg, 2000 Key words: semidefinite linear complementarity problem -P-property -GUS-property - Lyapunov nationallicence Mathematics Subject Classification (2000): 90C33, 93D05 nationallicence Gowda M. Seetharama Department of Mathematics & Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA, e-mail: gowda@math.umbc.edu, http://www.math.umbc.edu/˜gowda, US aut Song Yoon Department of Mathematics & Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA, e-mail: song@math.umbc.edu, US aut https://doi.org/10.1007/PL00011387 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00011387 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gowda M. Seetharama Department of Mathematics & Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA, e-mail: gowda@math.umbc.edu, http://www.math.umbc.edu/˜gowda, US aut NATIONALLICENCE 700 1- Song Yoon Department of Mathematics & Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA, e-mail: song@math.umbc.edu, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer