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.
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Supported by Natural Science Foundations of China (Grant No. 61179031 and 61401058)
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Duan, X.M., Sun, H.F. & Peng, L.Y. The α-geometric structures on manifold of positive definite Hermite matrices. Acta. Math. Sin.-English Ser. 30, 2137–2145 (2014). https://doi.org/10.1007/s10114-014-1285-x
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DOI: https://doi.org/10.1007/s10114-014-1285-x