On the existence of equiangular tight frames
Web14 de set. de 2015 · Abstract. An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a ... Web15 de out. de 2007 · We prove the existence of equiangular tight frames having n = 2 d-1 elements drawn from either C d or C d-1 whenever n is either 2 k-1 for k ∈ N, or a power of a prime such that n ≡ 3 mod 4. We also find a simple explicit expression for the prime power case by establishing a connection to a 2 d-element equiangular tight frame based on ...
On the existence of equiangular tight frames
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WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): WebA Grassmannian frame is a collection of unit vectors which are optimally incoherent. The most accessible (and perhaps most beautiful) of Grassmannian frames are equiangular tight frames (ETFs); indeed, there are infinite families of known ETFs, whereas only finitely many non-ETF Grassmannianframesare knownto date.
Webtight frame exists for each pair (d,N) with N ≤ 100 that meets the new conditions. The arguments also extend to deliver novel necessary conditions for the existence of equiangular tight frames whose Gram matrices have entries drawn from a discrete set of complex numbers. Index Terms—tight frame, equiangular lines, optimal Grassman- WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In a recent paper, Holmes and Paulsen established a necessary condition for the existence of an N …
WebComplex Equiangular Tight Frames Joel A. Troppa aMathematics Department, The University of Michigan, 530 Church St., Ann Arbor, MI 48109-1043, USA ... First, one could demonstrate the existence of specific complex ETFs via constructive (or nonconstructive) means. Second, one could attempt to rule out the possibility that a complex Web26 de fev. de 2014 · The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in ...
WebAbstract: An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and orthogonal rows of norm sqrt(N/d). Its key property is that the absolute inner …
Web开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 mid valley camera fairWeb1 de jan. de 2024 · For every V ≡ 1 or 3 mod 6 with V ≥ 3, there exists an equiangular tight frame of N vectors in C M with M = 1 6 ( V + 2) ( V + 3), N = 1 2 ( V + 1) ( V + 2). As illustrated by Tremain's original example above, this construction is real whenever the unimodular simplices come from real Hadamard matrices. In particular, a ( V + 1) × ( V + … mid valley behavioral care networkWeb29 de set. de 2010 · Doubly transitive equiangular tight frames that contain regular simplices. M. Fickus, Evan C. Lake. Mathematics. ArXiv. 2024. An equiangular tight … new teeth whitening solutionWeb1 de mar. de 2009 · The existence problems for the Mercedes–Benz systems and other more general equiangular tight frames are discussed. It is shown that the Welch inequality becomes the equality only on equiangular ... new teeth turkeyWebAn equiangular tight frame (ETF) is a d ×N matrix that has unit-norm columns and orthogonal rows of norm √ … new teeth todayWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and … mid valley california weatherWeb(equiangular lines, tight frame, ETF) may be expressed using only polynomials and an order-2 field automorphism (complex conjugation). From this light, our 1Elsewhere in the literature, “Zauner’s conjecture” may refer either to Conjecture 1.1 or to one of several stronger statements that posit the existence of equiangular lines with ... midvalley calvary chapel