#
On the monotonicity of weighted power means for matrices

On the monotonicity of weighted power means for matrices

Source title:

Linear Algebra and its Applications, 527: 128-140,
2017
(ISI)

Academic year of acceptance:

2016-2017

Abstract:

In this article, we provide an alternate proof of the fact that the weighted power means *μ*_{p}*A**, **B**, **t**t**A*^{p }*t**B*^{p}^{1}^{/}^{p}*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.