A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces

Constructing Packings in Projective Spaces and Grassmannian Spaces via Alternating Projection

This report presents a numerical method for finding good packings on spheres, in projective spaces, and in Grassmannian manifolds equipped with various metrics. In each case, producing a good packing is equivalent to constructing a matrix that has certain structural and spectral properties. By alternately enforcing the structural condition and then the spectral condition, it is frequently possi...

Constructing Packings in Grassmannian Manifolds via Alternating Projection

This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is equivalent to constructing a matrix that has certain structural and spectral properties. By alternately enforcing the structural condition and then the spectral condi...

Packing Planes in Four Dimensions and Other Mysteries

How should you choose a good set of (say) 48 planes in four dimensions? More generally, how do you find packings in Grassmannian spaces? In this article I give a brief introduction to the work that I have been doing on this problem in collaboration with A. R. Calderbank, J. We have found many nice examples of specific packings (70 4-spaces in 8-space, for instance), several general construction...

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

Grassmannian Frames with Applications to Coding and Communication

For a given class F of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation |〈fk, fl〉| among all frames {fk}k∈I ∈ F . We first analyze finite-dimensional Grassmannian frames. Using links to packings in Grassmannian spaces and antipodal spherical codes we derive bounds on the minimal achievable correlation for Grassmannian frames. These ...