Absil, P-AMahony, RobertSepulchre, R2015-12-132015-12-130167-8019http://hdl.handle.net/1885/77911We 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 spaceKeywords: Algorithms; Matrix algebra; Nonlinear equations; Optimization; Problem solving; Set theory; Theorem proving; Euclidean space; Grassmann manifolds; Invariant subspace; Newton method; Computational geometry Geodesic; Grassmann manifold; Invariant subspace; Levi-civita connection; Mean of subspaces; Newton method; Noncompact stiefel manifold; Parallel transportation; Principal fiber bundle200410.1023/B:ACAP.0000013855.14971.912015-12-11