On the exponential metric increasing property

Bhatia, Rajendra (2003) On the exponential metric increasing property Linear Algebra and its Applications, 375 . pp. 211-220. ISSN 0024-3795

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00243...

Related URL: http://dx.doi.org/10.1016/S0024-3795(03)00647-5


A short and simple proof is given for the inequality that shows that positive definite matrices constitute a Riemannian manifold of negative curvature. The idea of the proof leads to generalisations to non-Riemannian metrics, and to connections with some well-known inequalities of mathematical physics.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Positive Definite Matrix; Riemannian Manifold; Negative Curvature; Exponential Map; Geometric Mean; Unitarily Invariant Norm
ID Code:2599
Deposited On:08 Oct 2010 07:20
Last Modified:16 May 2016 13:34

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