CUED Publications database

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

Absil, P-A and Mahony, R and Sepulchre, R (2004) Riemannian geometry of Grassmann manifolds with a view on algorithmic computation. Acta Applicandae Mathematicae, 80. pp. 199-220. ISSN 0167-8019

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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 of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Item Type: Article
Uncontrolled Keywords: Geodesic Grassmann manifold Invariant subspace Levi-civita connection Mean of subspaces Newton method Noncompact stiefel manifold Parallel transportation Principal fiber bundle
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:28
Last Modified: 08 Dec 2014 02:14
DOI: 10.1023/B:ACAP.0000013855.14971.91