Geometry of midpoint sets for Thompson's metric

DOI10.1016/j.laa.2013.03.012zbMath1281.15038OpenAlexW2083054109MaRDI QIDQ389610

Yongdo Lim

Publication date: 21 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2013.03.012

zbMATH Keywords

convexityinvariant metricpositive definite matrixmidpointunitarily invariant normspectral normRiemannian trace metricThompson metricCartan-Hadamard Riemannian manifoldminimal geodesic

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Geodesics in global differential geometry (53C22)

Related Items (11)

On the nonlinear matrix equation X^p = A#_t(M^T (X^–1 + B)^–1 M) ⋮ Logarithmic mean of positive invertible operators ⋮ Linearity of Cartan and Wasserstein means ⋮ Geometric Matrix Midranges ⋮ Invariant tolerance relations on positive definite matrices ⋮ Minimal curves in \(\mathcal{U}(n)\) and \(\mathcal{G}l(n)^+\) with respect to the spectral and the trace norms ⋮ Unique geodesics for Thompson's metric ⋮ Operator inequalities and gyrolines of the weighted geometric means ⋮ The Karcher mean of three variables and quadric surfaces ⋮ The Karcher mean of equilateral triangles ⋮ Weighted inductive means

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