Connectivity and Irreducibility of Algebraic Varieties of Finite Unit Norm Tight Frames

14 Jan 2016  ·  Cahill Jameson, Mixon Dustin G., Strawn Nate ·

In this paper, we settle a long-standing problem on the connectivity of spaces of finite unit norm tight frames (FUNTFs), essentially affirming a conjecture first appearing in [Dykema and Strawn, 2003]. Our central technique involves continuous liftings of paths from the polytope of eigensteps 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, and also that generic FUNTFs are full spark. read more

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Functional Analysis