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 0167-8019Full text not available from this repository.
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.
|Uncontrolled Keywords:||Geodesic Grassmann manifold Invariant subspace Levi-civita connection Mean of subspaces Newton method Noncompact stiefel manifold Parallel transportation Principal fiber bundle|
|Divisions:||Div F > Control|
|Depositing User:||Cron job|
|Date Deposited:||04 Feb 2015 22:05|
|Last Modified:||09 Apr 2015 01:23|