NO DICE THEOREM ON SYMMETRIC CONES

Title
NO DICE THEOREM ON SYMMETRIC CONES
Author(s)
이호수금상호[금상호]임용도[임용도]
Keywords
EUCLIDEAN JORDAN ALGEBRAS; GEOMETRIC MEANS; SPECTRAL FUNCTIONS; OPTIMIZATION; MATRICES
Issue Date
201312
Publisher
MATHEMATICAL SOC REP CHINA
Citation
TAIWANESE JOURNAL OF MATHEMATICS, v.17, no.6, pp.1967 - 1982
Abstract
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.
URI
http://hdl.handle.net/YU.REPOSITORY/28023
ISSN
1027-5487
Appears in Collections:
기초교육대학 > 교양학부 > Articles
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE