The α-geometric structures on manifold of positive definite Hermite matrices

Xiao Min Duan, Hua Fei Sun, Linyu Peng

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Abstract

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 ±1-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.

Original languageEnglish
Pages (from-to)2137-2145
Number of pages9
JournalActa Mathematica Sinica, English Series
Volume30
Issue number12
DOIs
Publication statusPublished - 2014 Nov 7
Externally publishedYes

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Keywords

  • information geometry
  • optimal approximation
  • Positive definite Hermite matrices

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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