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Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank

✍ Scribed by Bonnabel, Silvère; Sepulchre, Rodolphe


Book ID
118059090
Publisher
Society for Industrial and Applied Mathematics
Year
2010
Tongue
English
Weight
252 KB
Volume
31
Category
Article
ISSN
0895-4798

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A Differential Geometric Approach to the
✍ Moakher, Maher 📂 Article 📅 2005 🏛 Society for Industrial and Applied Mathematics 🌐 English ⚖ 204 KB

In this paper we introduce metric-based means for the space of positive-definite matrices. The mean associated with the Euclidean metric of the ambient space is the usual arithmetic mean. The mean associated with the Riemannian metric corresponds to the geometric mean. We discuss some invariance pro