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Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation

Date

Authors

Absil, P-A

Mahony, Robert

Sepulchre, R

Publisher

Kluwer Academic Publishers

Abstract

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space

Keywords

Keywords: Algorithms; Matrix algebra; Nonlinear equations; Optimization; Problem solving; Set theory; Theorem proving; Euclidean space; Grassmann manifolds; Invariant subspace; Newton method; Computational geometry Geodesic; Grassmann manifold; Invariant subspace; Levi-civita connection; Mean of subspaces; Newton method; Noncompact stiefel manifold; Parallel transportation; Principal fiber bundle

URI

http://hdl.handle.net/1885/77911

Collections

Open Access Research

Source

Acta Applicandae Mathematicae

Type

Journal article

DOI

10.1023/B:ACAP.0000013855.14971.91