| Abstract: |
Let d > 1 be an integer and let R^d denote the Euclidean d-dimensional space equipped with the usual inner product (.,.). A set of n>1 lines, represented by the unit vectors v1, ..., vn is called equiangular, if there exists a constant A such that |(vi, vj)| = A for all 1 <= i < j <= n. We obtain several new results contributing to the theory of equiangular line systems in Euclidean spaces. Among other things, we present a new general lower bound on the number of equiangular lines; we describe the two-graphs on 12 vertices; and we investigate Seidel matrices with exactly three distinct eigenvalues. |
