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

arXiv2009.11240MaRDI QIDQ6349722

Du Dinh Nguyen

Publication date: 23 September 2020

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.

Has companion code repository: https://github.com/dnguyend/ManNullRange

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Real-valued functions on manifolds (58C05) Sensitivity analysis for optimization problems on manifolds (49Q12) Relations of manifolds and cell complexes with engineering (57Z20) Relations of manifolds and cell complexes with computer and data science (57Z25)

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