Riemannian gradient and Levi-Civita connection for fixed-rank matrices

2020/09/23 by Du Nguyễn, Nguyen, Du
Mathematics · Physics and Astronomy · Medicine · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2009.11240

Abstract

We provide formulas for Riemannian gradient and Levi-Civita connection for a family of metrics on fixed-rank matrix manifolds, based on nonconstant metrics on Stiefel manifolds.

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