On the existence of equiangular tight frames

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August undefined, 2024

Web1 de jul. de 2008 · Yet, despite their importance, we are far from having a complete understanding about the existence of equiangular tight frames. Some results can be found in [12,8,4,3,13,10,6,1,7,9,11]. A popular method to construct equiangular tight frames is based on conference matrices [8, 3,10]. Web1 de jul. de 2008 · Yet, despite their importance, we are far from having a complete understanding about the existence of equiangular tight frames. Some results can be …

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WebThe Internet Archive offers over 20,000,000 freely downloadable books and texts. There is also a collection of 2.3 million modern eBooks that may be borrowed by anyone with a free archive.org account. Borrow a Book Books on Internet Archive are … 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 … thepginc

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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 … Web3 Real equiangular tight frames In this section, we describe what is known about real equiangular tight frames. Throughout, we use ∃RETF(M,N) to denote the statement “there exists a real equiangular tight frame with parameters (M,N).” We start with some basic properties: Theorem 1 (see [39]). ∃RETF(M,N) implies each of the following: 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- the pgl movie

Tables of the existence of equiangular tight frames

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 … Webconstruction of equiangular tight frames for ﬁnite dimensional real Hilbert spaces [21, 18, 8, 3, 10], relatively few means are known for constructing equiangular frames in the complex case (see, e.g. [11, 17, 7]). The problem of the existence of equiangular frames is known to be equivalent thepgmclubWebEquiangular Tight Frames Let {x m} be a collection of N unit vectors in Cd with N ≥ d A lower bound on the maximum correlation between a pair of vectors: max m6= n hx m, x ni ≥ s N −d d(N −1) def= µ(d,N) The bound is met if and only if 1. The vectors are equiangular 2. The vectors form a tight frame sicily manteaux

"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 … " - On the existence of equiangular tight frames

On the existence of equiangular tight frames

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 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 …

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Web29 de set. de 2010 · Doubly transitive equiangular tight frames that contain regular simplices. M. Fickus, Evan C. Lake. Mathematics. ArXiv. 2024. An equiangular tight …

Web26 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 … 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 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 … 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 ...

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

Web31 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. sicily mansionsWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 sicily maintainerWebAbstract: 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 … sicily memory roamersWebd2 and a pair of ETFs (equiangular tight frames) in dimensions d(d± 1)/2. We also show that a WH (Weyl Heisenberg covariant) SIC in odd dimension dis naturally associated to a pair of symmetric tight fusion frames in dimension d. We deduce two relaxations of the WH SIC existence problem. We also ﬁnd a reformulation of the problem in which ... sicily medusaWebis an equiangular tight frame for R(M N). We call this the complementary equiangular tight frame. It follows that equiangular tight frames come in pairs and if M>2Nthen M<2(M N). So we only need to classify the equiangular tight frames for M>2N. Certain classes of equiangular tight frames always exist. Proposition 3.3: RN always has an 1. sicily may weatherWeb9 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 ... sicily may 2023WebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the … sicily meatballs