Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition

DOI10.1137/18M1221084WikidataQ115246925 ScholiaQ115246925MaRDI QIDQ5203964

Zhenhua Lin

Publication date: 9 December 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.09326

zbMATH Keywords

Lie groupparallel transportCholesky decompositionFréchet meansymmetric positive definite matrixbi-invariant metriclower triangular matrix

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Geodesics in global differential geometry (53C22) Differential geometry of symmetric spaces (53C35) Means (26E60) Lie groups (22E99) Matrix pencils (15A22) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (16)

Theoretically and Computationally Convenient Geometries on Full-Rank Correlation Matrices ⋮ Intrinsic Riemannian functional data analysis for sparse longitudinal observations ⋮ Concurrent object regression ⋮ The geometry of mixed-Euclidean metrics on symmetric positive definite matrices ⋮ Bures–Wasserstein Minimizing Geodesics between Covariance Matrices of Different Ranks ⋮ Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference ⋮ Negativizability: a useful property for distributed state estimation and control in cyber-physical systems ⋮ \(O(n)\)-invariant Riemannian metrics on SPD matrices ⋮ Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry ⋮ Structure‐preserving invariant interpolation schemes for invertible second‐order tensors ⋮ K-splines on SPD manifolds ⋮ Spatiotemporal analysis using Riemannian composition of diffusion operators ⋮ Restricted Riemannian geometry for positive semidefinite matrices ⋮ A Stein's approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric ⋮ Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics ⋮ Total variation regularized Fréchet regression for metric-space valued data

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