Journal
ACTA APPLICANDAE MATHEMATICAE
Volume 80, Issue 2, Pages 199-220Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/B:ACAP.0000013855.14971.91
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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.
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