Title

Geodesic in-betweenness for means of several matrices

Document Type

Article

Publication Date

3-1-2022

Subject Area

ARRAY(0x557373598948)

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

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