Riemannian geometry and matrix geometric means
โ Scribed by Rajendra Bhatia; John Holbrook
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 338 KB
- Volume
- 413
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
Contact Riemannian geometry is used to study equilibrium thermodynamical systems as embedded submanifolds of the thermodynamical phase space. A metric compatible with the contact structure is chosen and proved to be invariant under Legendre transformations. With this metric structure all curvature i
We define a new family of matrix means {L ฮผ (ฯ; A)} ฮผโR where ฯ and A vary over all positive probability vectors in R m and m-tuples of positive definite matrices resp. Each of these means interpolates between the weighted harmonic mean (ฮผ = -โ) and the arithmetic mean of the same weight (ฮผ = โ) wit