Reference : Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/33242
Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
English
Absil, P.-A. [> > > >]
Mahony, R. [> > > >]
Sepulchre, Rodolphe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Jan-2004
Acta Applicandae Mathematicae
Kluwer Academic Publ
80
2
199-220
Yes
International
0167-8019
Dordrecht
[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.
http://hdl.handle.net/2268/33242
10.1023/B:ACAP.0000013855.14971.91
http://www.springerlink.com/content/q6356j236hpn3579/

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