Rank-preserving geometric means of positive semi-definite matrices

DOI10.1016/j.laa.2012.12.009zbMath1267.15028arXiv1007.5494OpenAlexW2123603517MaRDI QIDQ1947084

Anne Collard, Silvère Bonnabel, Rodolphe J. Sepulchre

Publication date: 12 April 2013

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.5494

zbMATH Keywords

Riemannian geometrygeometric meanrankfactorizationpositive semi-definite matricesorthogonal matricesKarcher meanmatrix meansprincipal anglesRiemann mean

Mathematics Subject Classification ID

Factorization of matrices (15A23) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Means (26E60) Vector spaces, linear dependence, rank, lineability (15A03) Operator means involving linear operators, shorted linear operators, etc. (47A64) Orthogonal matrices (15B10)

Related Items

Anisotropy preserving DTI processing, Restricted Riemannian geometry for positive semidefinite matrices, Geometric mean and geodesic regression on Grassmannians, On Procrustes matching of non-negative matrices and an application to random tomography, Quotient Geometry with Simple Geodesics for the Manifold of Fixed-Rank Positive-Semidefinite Matrices

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