Article (Scientific journals)
Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
Absil, P.-A.; Mahony, R.; Sepulchre, Rodolphe
2004In Acta Applicandae Mathematicae, 80 (2), p. 199-220
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Abstract :
[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 :
80
Issue :
2
Pages :
199-220
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 21 December 2009

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