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Geodesics for dual connections and means on symmetric cones

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Publication:1764272
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DOI10.1007/s00020-003-1245-9zbMath1073.47512OpenAlexW1996945827MaRDI QIDQ1764272

Atsumi Ohara

Publication date: 24 February 2005

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-003-1245-9


zbMATH Keywords

geodesicmeanaffine connectionsymmetric cone


Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Operator means involving linear operators, shorted linear operators, etc. (47A64) Associated geometries of Jordan algebras (17C37)


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Exponential arcs in the manifold of vector states on a \(\sigma\)-finite von Neumann algebra ⋮ Geometric mean of probability measures and geodesics of Fisher information metric ⋮ Doubly autoparallel structure and curvature integrals. Applications to iteration complexity for solving convex programs ⋮ Quasi-arithmetic centers, quasi-arithmetic mixtures, and the Jensen-Shannon \(\nabla \)-divergences ⋮ Unnamed Item ⋮ Information geometry of the space of probability measures and barycenter maps




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