Monotonicity of the matrix geometric mean

Bhatia, Rajendra ; Karandikar, Rajeeva L. (2011) Monotonicity of the matrix geometric mean Mathematische Annalen . ISSN 0025-5831

Full text not available from this repository.

Official URL:

Related URL:


An attractive candidate for the geometric mean of m positive definite matrices A1, . . . , Am is their Riemannian barycentre G. One of its important operator theoretic properties, monotonicity in the m arguments, has been established recently by Lawson and Lim. We give an elementary proof of this property using standard matrix analysis and some counting arguments. We derive some new inequalities for G. One of these says that, for any unitarily invariant norm, ||| G ||| is not bigger than the geometric mean of |||A 1|||, . . . , |||A m |||.

Item Type:Article
Source:Copyright of this article belongs to Springer.
ID Code:73307
Deposited On:02 Dec 2011 08:39
Last Modified:16 Feb 2013 06:31

Repository Staff Only: item control page