Title

Some geometric properties of matrix means with respect to different metrics

Document Type

Article

Publication Date

11-1-2020

Subject Area

ARRAY(0x55e5821de040)

Abstract

In this paper we study the monotonicity, in-betweenness and in-sphere properties of matrix means with respect to Bures–Wasserstein, Hellinger and log-determinant metrics. More precisely, we show that the matrix power means (Kubo–Ando and non-Kubo–Ando extensions) satisfy the in-betweenness property in the Hellinger metric. We also show that for two positive definite matrices A and B, the curve of weighted Heron means, the geodesic curve of the arithmetic and the geometric mean lie inside the sphere centered at the geometric mean with the radius equal to half of the log-determinant distance between A and B.

Publication Title

Positivity

Volume

24

Issue

5

First Page

1419

Last Page

1434

Digital Object Identifier (DOI)

10.1007/s11117-020-00738-w

ISSN

13851292

E-ISSN

15729281

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