The one thing I don't agree with in this paper is the claim that because the geodesic distance between two k-planes P, Q in R^n (in the Grassmannian manifold of k-planes in R^n) is not differentiable at some points (it's given by d(P,Q) = sqrt( theta_1^2 + . . . + theta_n^2) ) it is therefore flawed. All the most basic widely accepted distances -- geodesic distances on any smooth Riemannian manifold, including the Euclidean distance on R^n -- e.g., D(x,y) := |x-y| on R -- have this "flaw". --Dan << In case you haven't read the paper below, you should give a look: "Packing lines, planes ..." by Conway, Hardin and Sloane. http://www2.research.att.com/~njas/doc/grass.pdf
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