Polytopes of eigensteps of finite equal norm tight frames
Combinatorics
2017-11-30 v2 Functional Analysis
Metric Geometry
Abstract
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand-Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope.
Keywords
Cite
@article{arxiv.1507.04197,
title = {Polytopes of eigensteps of finite equal norm tight frames},
author = {Tim Haga and Christoph Pegel},
journal= {arXiv preprint arXiv:1507.04197},
year = {2017}
}
Comments
14 pages, 6 figures