Monotonic properties of the least squares mean
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 mean and derive our results in this more general setting. © 2010 Springer-Verlag.
Publication Source (Journal or Book title)
Lawson, J., & Lim, Y. (2011). Monotonic properties of the least squares mean. Mathematische Annalen, 351 (2), 267-279. https://doi.org/10.1007/s00208-010-0603-6