References of "Acta Applicandae Mathematicae"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailRiemannian geometry of Grassmann manifolds with a view on algorithmic computation
Absil, P.-A.; Mahony, R.; Sepulchre, Rodolphe ULg

in Acta Applicandae Mathematicae (2004), 80(2), 199-220

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 ... [more ▼]

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. [less ▲]

Detailed reference viewed: 40 (5 ULg)