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Packing Lines, Planes, etc.: Packings in Grassmannian Space

J. H. Conway·R. H. Hardin·N. J. A. Sloane
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Abstract

This paper addresses the question: how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of N, n, m are described, as well as a reformulation of the problem that was suggested by these computations. The reformulation gives a way to describe n-dimensional subspaces of m-space as points on a sphere in dimension (m-1)(m+2)/2, which provides a (usually) lower-dimensional representation than the Pluecker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multi-dimensional data via Asimov's "Grand Tour" method.

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J. H. Conway, R. H. Hardin, N. J. A. Sloane. 2002-08-01. Packing Lines, Planes, etc.: Packings in Grassmannian Space. https://arxiv.org/abs/math/0208004

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