> \pJava Excel API v2.6 Ba==h\:#8X@"1Arial1Arial1Arial1Arial + ) , * `vDC, title[*]contributor[*]keywords[*]date[issued] publisher citationsidentifier[uri]identifier[doi]abstract"NO DICE THEOREM ON SYMMETRIC CONESt8;
8[8];
ǩĳ[ǩĳ];WEUCLIDEAN JORDAN ALGEBRAS;
GEOMETRIC MEANS;
SPECTRAL FUNCTIONS;
OPTIMIZATION;
MATRICES;201312MATHEMATICAL SOC REP CHINA<TAIWANESE JOURNAL OF MATHEMATICS, v.17, no.6, pp.1967 - 1982)http://hdl.handle.net/YU.REPOSITORY/28023cThe monotonicity of the least squares mean on the Riemannian manifold of positive definite matrices, conjectured by Bhatia and Holbrook and one of key axiomatic properties of matrix geometric means, was recently established based on the Strong Law of Large Number [14, 4]. A natural question concerned with the S.L.L.N is so called the no dice conjecture. It is a problem to make a construction of deterministic sequences converging to the least squares mean without any probabilistic arguments. Very recently, Holbrook [7] gave an affirmative answer to the conjecture in the space of positive definite matrices. In this paper, inspired by the work of Holbrook [7] and the fact that the convex cone of positive definite matrices is a typical example of a symmetric cone (self-dual homogeneous convex cone), we establish the no dice theorem on general symmetric cones.>5WPrez8Ik +@b25
2n
dMbP?_*+%" ,,??U
$~>@
Root EntryWorkbookSummaryInformation( DocumentSummaryInformation8