Geodesic in-betweenness for means of several matrices
Document Type
Article
Publication Date
3-1-2022
Abstract
A matrix mean σ is said to satisfy the in-betweenness property with respect to the metric d if for any pair of positive definite matrices A and B, d(A,AσB)≤d(A,B). In this article, we introduce the geodesic in-betweenness property for k-tuples of positive definite matrices with respect to any metric. Moreover, we show that in spaces of non-positive curvature, geodesic in-betweenness implies in-betweenness in the case of two matrices. We then show some examples of metrics and means for which this property is satisfied.
Publication Title
Linear Algebra and Its Applications
Volume
636
First Page
77
Last Page
92
Digital Object Identifier (DOI)
10.1016/j.laa.2021.11.017
ISSN
00243795
Citation Information
Dumitru, R., Franco, J.A. (2022) Geodesic in-betweenness for means of several matrices. Linear Algebra and Its Applications, 636, 77-92. https://doi.org/10.1016/j.laa.2021.11.017