TY - JOUR
AU - 이호수
AU - 금상호[금상호]
AU - 임용도[임용도]
DA - 201312
UR - http://hdl.handle.net/YU.REPOSITORY/28023
AB - The 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.
LA - 영어
PB - MATHEMATICAL SOC REP CHINA
KW - EUCLIDEAN JORDAN ALGEBRAS
KW - GEOMETRIC MEANS
KW - SPECTRAL FUNCTIONS
KW - OPTIMIZATION
KW - MATRICES
TI - NO DICE THEOREM ON SYMMETRIC CONES
ER -