# Publications and Preprints

On the exponential metric increasing property
by
Rajendra Bhatia
The metric increasing property of the exponential map is known to be equivalent to the fact that the set of positive definite matrices is a Riemannian manifold of nonpositive curvature. We show that this property is an easy consequence of the logarithmic-geometric mean inequality for positive numbers. Operator versions of this inequality lead to a generalisation of the exponential metric increasing property to all Schatten-von Neumann norms.

isid/ms/2002/14 [fulltext]