Geodesic in-betweenness for means of several matrices
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.
Linear Algebra and Its Applications
Digital Object Identifier (DOI)
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