Connectivity of spaces of finite unit-norm tight frames

Jameson Cahill; Dustin Mixon; Nate Strawn

doi:10.1117/12.2189595

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11 September 2015 Connectivity of spaces of finite unit-norm tight frames

Jameson Cahill, Dustin Mixon, Nate Strawn

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Proceedings Volume 9597, Wavelets and Sparsity XVI; 95971A (2015) https://doi.org/10.1117/12.2189595
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

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.

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Jameson Cahill, Dustin Mixon, and Nate Strawn "Connectivity of spaces of finite unit-norm tight frames", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95971A (11 September 2015); https://doi.org/10.1117/12.2189595

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