Structure of Hiai-Petz parametrized geometry for positive definite matrices

DOI10.1016/J.LAA.2009.08.009zbMath1179.53027OpenAlexW1973308254WikidataQ112882170 ScholiaQ112882170MaRDI QIDQ1044609

Jun Ichi Fujii

Publication date: 18 December 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.08.009

zbMATH Keywords

positive definite matricesgeodesicFinsler geometryunitarily invariant normoperator mean

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (4)

Relative Operator Entropy ⋮ Path of quasi-means as a geodesic ⋮ Generalized Pólya-Szegő type inequalities for some non-commutative geometric means ⋮ Means for fixed rank PSD matrices

Cites Work

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• Riemannian geometry and matrix geometric means
• Riemannian metrics on positive definite matrices related to means
• Means of positive linear operators
• Means of Hilbert space operators
• Differential and metrical structure of positive operators
• GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS

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