On the existence of equiangular tight frames

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WebAn equiangular tight frame (ETF) is a d ×N matrix that has unit-norm columns and orthogonal rows of norm √ …

arXiv:1402.6429v1 [math.FA] 26 Feb 2014

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 … WebIt is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. danbury ct hotels listing

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Webframes and strongly regular graphs of a certain type, it has been veriﬁed that a real equiangular tight frame exists for each pair (d,N) with N ≤ 100 that meets the new … http://users.cms.caltech.edu/~jtropp/slides/Tro05-Complex-Equiangular-Talk.pdf WebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the … birds of passage 意味

$arXiv:0805.2014v2 [math.FA] 1 Sep 2008$

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Web1 de abr. de 2015 · A table of these equiangular tight frames, as well as a review of many of the known constructions, may be found in [29]. As an example, one may always … Web(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 ... birds of passage movie reviewWebSequences, or optimal Grassmannian frames, or two-uniform frames. We prefer the more descriptive term “equiangular tight frame.” 1.1 Summary of Results The numerical evidence suggests that ETFs do not arise for most pairs (d,N). See [21, Sec. V-C] for details of this investigation. The goal of the present paper birds of passage refers to those who

"WebSequences, or optimal Grassmannian frames, or two-uniform frames. We prefer the more descriptive term “equiangular tight frame.” 1.1 Summary of Results The numerical … " - On the existence of equiangular tight frames

On the existence of equiangular tight frames

All complex equiangular tight frames in dimension 3

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and … Web1 de abr. de 2015 · Tables of the existence of equiangular tight frames. A Grassmannian frame is a collection of unit vectors which are optimally incoherent. To date, the vast …

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Web25 de fev. de 2009 · A survey on equiangular tight frames in the space $$ \\mathbb{R}^n $$ is presented. Several equivalent definitions of a tight frame are given. The … WebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. 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 tight frames (if ...

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 ... Web1 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 + …

Web9 de abr. de 2024 · a so-called equiangular tight frame if and only if this lower. bound is saturated, meaning in particular that the subnor-malised projectors {d. n ... deciding the existence of EAMs (see e.g. [68 ... 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

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and …

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 … danbury ct humane societyWeb15 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 ... danbury ct help wantedWeb31 de mar. de 2024 · Title: Small projective codes and equiangular lines Abstract: How can one arrange $d+k$ many vectors in $\mathbb{R}^d$ so that they are as close to orthogonal as possible? Such arrangements are known as projective codes (or antipodal spherical codes) and are a natural generalization of balanced error-correcting codes. birds of patagonia chileWebComplex 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 birds of pennsylvania listWeb6 de ago. de 2012 · An equiangular tight frame (ETF) is a d * n matrix that has orthogonal rows and unit-norm columns. ETFs have applications in communications, coding theory and quantum computing. birds of passage movie 2018WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): birds of perth suburbsWeb26 de fev. de 2024 · Abstract An equiangular tight frame (ETF) is an equal norm tight frame with the same sharp angles between the vectors. This work is an attempt to create a brief review with complete proofs and calculations of two directions of research on the equiangular tight frames (ETF): bounds of the spark of the ETF, namely the smallest … birds of pennsylvania book