The \(\alpha\)-geometric structures on manifold of positive definite Hermite matrices
type: Item
instance of: scholarly article
title: The \(\alpha\)-geometric structures on manifold of positive definite Hermite matrices
zbMATH Open document ID: 1315.53013
author: Xiaomin Duan
author: Huafei Sun
author: Linyu Peng
publication date: 2014-12-10T00:00:00Z
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 62B10
zbMATH DE Number: 6378999
zbMATH Keywords: positive definite Hermite matrices
zbMATH Keywords: information geometry
zbMATH Keywords: optimal approximation
MaRDI profile type: Publication
full work available at URL: s10114-014-1285-x
OpenAlex ID: W2029800196
cites work: Differential-geometrical methods in statistics
cites work: Q4527387
cites work: Information geometry on hierarchy of probability distributions
cites work: Finiteness of mapping degree sets for 3-manifolds
cites work: Iterative approximation of statistical distributions and relation to information geometry
cites work: On self-mapping degrees of \(S^{3}\)-geometry manifolds
cites work: Dualistic differential geometry of positive definite matrices and its applications to related problems
cites work: A natural gradient descent algorithm for the solution of discrete algebraic Lyapunov equations based on the geodesic distance
cites work: Riemannian gradient algorithm for the numerical solution of linear matrix equations
cites work: A natural gradient algorithm for the solution of Lyapunov equations based on the geodesic distance
cites work: Jacobi fields on the manifold of nonsingular Hermite matrices
cites work: Q4327858
cites work: ON THE CURVATURE OF A CERTAIN RIEMANNIAN SPACE OF MATRICES
cites work: The geometric structures and instability of entropic dynamical models
cites work: INFORMATION GEOMETRY AND PHASE TRANSITIONS
cites work: Hamilton-type gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
cites work: Q4980560
DOI: 10.1007/S10114-014-1285-X
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 6378999