TY - JOUR
T1 - The α-geometric structures on manifold of positive definite Hermite matrices
AU - Duan, Xiao Min
AU - Sun, Hua Fei
AU - Peng, Lin Yu
N1 - Funding Information:
Received May 30, 2011, accepted March 4, 2014 Supported by Natural Science Foundations of China (Grant No. 61179031 and 61401058)
Publisher Copyright:
© 2014, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.
PY - 2014/11/7
Y1 - 2014/11/7
N2 - 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.
AB - 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.
KW - Positive definite Hermite matrices
KW - information geometry
KW - optimal approximation
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U2 - 10.1007/s10114-014-1285-x
DO - 10.1007/s10114-014-1285-x
M3 - Article
AN - SCOPUS:84911463716
SN - 1439-8516
VL - 30
SP - 2137
EP - 2145
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 12
ER -