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Proceedings Paper

Connectivity of spaces of finite unit-norm tight frames
Author(s): Jameson Cahill; Dustin Mixon; Nate Strawn
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Paper Abstract

We show that the spaces of finite unit norm tight frames are connected, which verifies a conjecture first appearing in Dykema and Strawn (2006). Our central technique involves continuous liftings of paths from the polytope of eigensteps (see Cahill et al., 2012), or Gelfand-Tsetlin patterns, to spaces of FUNTFs. After demonstrating this connectivity result, we refine our analysis to show that the set of nonsingular points on these spaces is also connected, and we use this result to show that spaces of FUNTFs are irreducible in the algebro-geometric sense.

Paper Details

Date Published: 11 September 2015
PDF: 12 pages
Proc. SPIE 9597, Wavelets and Sparsity XVI, 95971A (11 September 2015); doi: 10.1117/12.2189595
Show Author Affiliations
Jameson Cahill, New Mexico State Univ. (United States)
Dustin Mixon, Air Force Institute of Technology (United States)
Nate Strawn, Georgetown Univ. (United States)

Published in SPIE Proceedings Vol. 9597:
Wavelets and Sparsity XVI
Manos Papadakis; Vivek K. Goyal; Dimitri Van De Ville, Editor(s)

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