Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773387 | Linear Algebra and its Applications | 2017 | 13 Pages |
Abstract
In this article, we provide an alternate proof of the fact that the weighted power means μp(A,B,t)=(tAp+(1ât)Bp)1/p, 1â¤pâ¤2 satisfy Audenaert's “in-betweenness” property for positive semidefinite matrices. We show that the “in-betweenness” property holds with respect to any unitarily invariant norm for p=1/2 and with respect to the Euclidean metric for p=1/4. We also show that the only Kubo-Ando symmetric mean that satisfies the “in-betweenness” property with respect to any metric induced by a unitarily invariant norm is the arithmetic mean. Finally, for p=6 we give a counterexample to a conjecture by Audenaert regarding the “in-betweenness” property.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Trung Hoa Dinh, Raluca Dumitru, Jose A. Franco,