Abstract
We prove that a trace function, generated by the functional calculus, is geodesically convex in the Riemannian manifold of positive definite matrices, if and only if it is geodesically convex in positive numbers. The analysis of multivariate operator means is facilitated by the study of classes of means that are fix-points under a contraction with respect to the Thompson metric. Although such methods are powerful, they crucially depend on monotonicity. We develop new techniques to prove existence of multivariate operator means that are not necessarily monotone.
Original language | English |
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Pages (from-to) | 209-224 |
Number of pages | 16 |
Journal | Linear Algebra and Its Applications |
Volume | 564 |
DOIs | |
Publication status | Published - 2019 Mar 1 |
Keywords
- Convex-log function
- Geodesically convex function
- Hyper-mean
- Multivariate operator mean
- Operator mean
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics