Equiangular Lines in Low Dimensional Euclidean Spaces

Equiangular lines in Euclidean spaces

Equiangular subspaces in Euclidean spaces

A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in R was studied extensively for the last 70 years. In this paper, we study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum s...

Lines in n-Dimensional Euclidean Spaces

In this paper, we define the line of n-dimensional Euclidean space and we introduce basic properties of affine space on this space. Next, we define the inner product of elements of this space. At the end, we introduce orthogonality of lines of this space. provide the terminology and notation for this paper. (4) (a · b) · x = a · (b · x). (6) a · (x 1 + x 2) = a · x 1 + a · x 2. (7) (a + b) · x ...

Equiangular Lines and Spherical Codes in Euclidean Space

A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R was extensively studied for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, in this paper we prove that for every fixed angle θ and sufficiently large n there are at most 2n−...

Large Equiangular Sets of Lines in Euclidean Space

A construction is given of 29(d + 1) 2 equiangular lines in Euclidean d-space, when d = 3 · 22t−1 − 1 with t any positive integer. This compares with the well known “absolute” upper bound of 12d(d+ 1) lines in any equiangular set; it is the first known constructive lower bound of order d2 . For background and terminology we refer to Seidel [3]. The standard method for obtaining a system of equi...