Monotonic Properties of the Least Squares Mean
Metric Geometry
2010-07-28 v1 Rings and Algebras
Abstract
We settle an open problem of several years standing by showing that the least-squares mean for positive definite matrices is monotone for the usual (Loewner) order. Indeed we show this is a special case of its appropriate generalization to partially ordered complete metric spaces of nonpositive curvature. Our techniques extend to establish other basic properties of the least squares mean such as continuity and joint concavity. Moreover, we introduce a weighted least squares means and extend our results to this setting.
Keywords
Cite
@article{arxiv.1007.4792,
title = {Monotonic Properties of the Least Squares Mean},
author = {Jimmie Lawson and Yongdo Lim},
journal= {arXiv preprint arXiv:1007.4792},
year = {2010}
}
Comments
21 pages