Absil, PA 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.
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|Date Deposited:||09 Dec 2016 17:25|
|Last Modified:||25 Feb 2017 22:21|