On the existence of equiangular tight frames
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. 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:
On the existence of equiangular tight frames
Did you know?
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. 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 …
Web22 de out. de 2014 · In a recent paper, Holmes and Paulsen established a necessary condition for the existence of an N-vector equiangular tight frame in a d-dimensional … 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 …
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 ... 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
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
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]). sharif scotlandWebis 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 … poppin in to say happy valentine\u0027s dayWebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the … sharif schoolWeb1 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 … sharif scottish cricketerWebtight 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 … sharif scotland cricketerWebIt 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. poppin hut thunder bayWeb1 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 + … sharifs burnley menu