The Karcher mean of equilateral triangles

DOI10.1016/j.laa.2022.10.014OpenAlexW4306179826MaRDI QIDQ2093527

Yongdo Lim, Eduardo Ghiglioni

Publication date: 8 November 2022

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

Full work available at URL: https://doi.org/10.1016/j.laa.2022.10.014

zbMATH Keywords

equilateral trianglepositive definite matrixtensor productRiemannian trace metricKarcher meanC-S factorization

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Linear operator inequalities (47A63) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Global Riemannian geometry, including pinching (53C20)

Cites Work

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• Monotonic properties of the least squares mean
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• Finsler structures for the part metric and Hilbert's projective metric and applications to ordinary differential equations
• Geometric means
• Invariant tolerance relations on positive definite matrices
• Analyticity of the Karcher mean coefficient maps
• From hyperbolic geometry to \(2\times 2\) Hermitian matrices and back
• Hyperbolicity of the Karcher mean
• The Karcher mean of linearly independent triples
• Hilbert and Thompson isometries on cones in JB-algebras
• Karcher means and Karcher equations of positive definite operators
• Hilbert’s projective metric and iterated nonlinear maps

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