On the existence of equiangular tight frames
Web1 de out. de 2007 · Request PDF On the existence of equiangular tight frames An equiangular tight frame (ETF) is a d×N matrix that has unit-norm columns and … 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 …
On the existence of equiangular tight frames
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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 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 …
WebAn equiangular tight frame (ETF) is a d ×N matrix that has unit-norm columns and orthogonal rows of norm √ … WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda):
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. Web17 de jul. de 2004 · Using a new one-to-one correspondence between equivalence classes of real equiangular tight frames and strongly regular graphs of a certain type, it has been veri ed that a real equiangular tight ...
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 + …
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. rumus breaking point theoryWebtight 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- rumus backgroundWeb4 de ago. de 2015 · Neither the existence of SIC-POVMs in higher-dimensional Hilbert spaces nor the nonexistence of MUBs in a six-dimensional Hilbert space has been proved. On the other hand, conditional SIC-POVMs are considered as equiangular tight frames. The existence of equiangular tight frames is also studied in many literature (e.g., [8, … scary movie mash potatoesWebAbstract: 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 … rumus black scholesWebFinally, 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]). scary movie midsummerWebEquiangular 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 scary movie michael myersWeb15 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 … scary movie miss man actor