Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

[en] 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 R-n. In these formulas, p-planes are represented as the column space of n x 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.

Disciplines :

Mathematics

Author, co-author :

Absil, P.-A.

Mahony, R.

Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Language :

English

Title :

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

Publication date :

January 2004

Journal title :

Acta Applicandae Mathematicae

ISSN :

0167-8019

eISSN :

1572-9036

Publisher :

Kluwer Academic Publ, Dordrecht, Netherlands

Volume :

Issue :

Pages :

199-220

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://www.springerlink.com/content/q6356j236hpn3579/

Available on ORBi :

since 21 December 2009

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Scopus citations^®

272

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250

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199

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382

Bibliography

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