Preserving problems of geodesic-affine maps and related topics on positive definite matrices

DOI10.1016/j.laa.2015.06.009zbMath1339.47052OpenAlexW882261526MaRDI QIDQ490898

Ming-Cheng Tsai, Patrícia Szokol, Jun Zhang

Publication date: 21 August 2015

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

Full work available at URL: https://doi.org/10.1016/j.laa.2015.06.009

zbMATH Keywords

Riemannian metricrelative entropypositive definite matricesgeodesic-affine mappreserving problems

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Geodesics in global differential geometry (53C22) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items

Maps between the positive definite cones of operator algebras preserving a norm of a geodesic correspondence ⋮ Preserver problems related to quasi-arithmetic means of invertible positive operators ⋮ Maps preserving Schatten norms of power means of positive operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Order automorphisms on positive definite operators and a few applications
• Riemannian geometry and matrix geometric means
• Riemannian metrics on positive definite matrices related to means
• Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in \(C^\ast\)-algebras
• Riemannian metrics on positive definite matrices related to means. II
• Isometries of the geodesic distances for the space of invertible positive operators and matrices
• Linear transformations which preserve Hermitian matrices
• Dualistic differential geometry of positive definite matrices and its applications to related problems
• Jordan triple endomorphisms and isometries of spaces of positive definite matrices
• Maps preserving the geometric mean of positive operators
• The Geometric Mean, Matrices, Metrics, and More
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Operator differentiable functions

This page was built for publication: Preserving problems of geodesic-affine maps and related topics on positive definite matrices