On the existence of equiangular tight frames

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Webis 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. 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.

EQUIANGULAR TIGHT FRAMES - Springer

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 ... WebFinally, we mention a general necessary condition for the existence of equiangular tight frames. Compared to the local conditions described above, it is a global condition depending on solely the parameters n and m. Theorem 2.5 (Naimark, see e.g. [7]). how does multiple myeloma manifest

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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 … 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 … 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 … how does multiverse make money

CiteSeerX — On the existence of equiangular tight frames

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: 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 how does multiple myeloma affect the bonesWebThe 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 ... photo of kevin costner

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

On the existence of equiangular tight frames

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]. 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.

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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 … 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 ...

WebEquiangular 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 Web1 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 ...

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 …

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 …

Web6 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. how does multiple left join worksWeb29 de set. de 2010 · Doubly transitive equiangular tight frames that contain regular simplices. M. Fickus, Evan C. Lake. Mathematics. ArXiv. 2024. An equiangular tight … how does multiplexing affect bandwidthWebconstruction 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 how does multiple myeloma startWeb1 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 + … how does multitasking cause stresshttp://users.cms.caltech.edu/~jtropp/slides/Tro05-Complex-Equiangular-Talk.pdf how does multiple myeloma show up on pet scanWeb15 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 ... how does multisensory integration workWeb1 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 … how does multitasking affect memory