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arXiv · 1507.04197

Polytopes of eigensteps of finite equal norm tight frames

Tim Haga·Christoph Pegel
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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.

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Tim Haga, Christoph Pegel. 2016-06-19. Polytopes of eigensteps of finite equal norm tight frames. https://doi.org/10.1007/s00454-016-9799-x

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