The α-Geometric Structures on Manifold of Positive Definite Hermite Matrices  

作　　者：Xiao Min DUAN Hua Fei SUN Lin Yu PENG 

机构地区：[1]Department of Mathematics,Beijing Institute of Technology [2]School of Science,Dalian Jiaotong University [3]Department of Mathematics,University of Surrey,Guildford,Surrey GU2 7XH,UK

出　　处：《Acta Mathematica Sinica,English Series》2014年第12期2137-2145,共9页数学学报（英文版）

基　　金：Supported by Natural Science Foundations of China(Grant No.61179031 and 61401058)

摘　　要：Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry.A Riemannian metric is defined and dual α-connections are introduced.Then the fact that the manifold is ±l-flat is shown.Moreover,the divergence of two points on the manifold is given through dual potential functions.Furthermore,the optimal approximation of a point onto the submanifold is gotten.Finally,some simulations are given to illustrate our results.Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry.A Riemannian metric is defined and dual α-connections are introduced.Then the fact that the manifold is ±l-flat is shown.Moreover,the divergence of two points on the manifold is given through dual potential functions.Furthermore,the optimal approximation of a point onto the submanifold is gotten.Finally,some simulations are given to illustrate our results.

关 键 词：Positive definite Hermite matrices information geometry optimal approximation 

分 类 号：O151.21[理学—数学] TN919.3[理学—基础数学]