Abstract
Abstract
We define frames for a finite dimensional Hilbert space ℍ as the complete systems in ℍ. An equiangular tight frame (ETF) is an equal norm tight frame with the same sharp angles between the vectors. A regular simplex is a special type of ETF in which the number of vectors is one more than the dimension of the space they span. A detailed and independent from other sources presentation of recent results by M. Fickus, J. Jasper, E. J. King and D. G. Mixon is given, in which a lower bound for the spark of the system of equal norm vectors is obtained using the restricted isometry property. The existence of the regular s-simplices for an arbitrary positive integer s is proved using Naimark complement. A review of recent results towards resolving the known Paulsen problem is given.
Subject
General Physics and Astronomy
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