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

Xiao Min Duan, Hua Fei Sun, Linyu Peng

1 引用 (Scopus)

### 抄録

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.

元の言語 English 2137-2145 9 Acta Mathematica Sinica, English Series 30 12 https://doi.org/10.1007/s10114-014-1285-x Published - 2014 11 7 Yes

### Fingerprint

Geometric Structure
Hermite
Positive definite
Geometry
Information Geometry
Optimal Approximation
Riemannian Metric
Potential Function
Submanifolds
Divergence
Simulation

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### これを引用

The α-geometric structures on manifold of positive definite Hermite matrices. / Duan, Xiao Min; Sun, Hua Fei; Peng, Linyu.

：: Acta Mathematica Sinica, English Series, 巻 30, 番号 12, 07.11.2014, p. 2137-2145.

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