Enumeration of Seidel matrices

TL;DR

This paper investigates Seidel matrices, determining their spectral properties for small orders, classifies those with three eigenvalues up to order 23, and applies findings to equiangular lines in 12-dimensional space.

Contribution

It provides new classifications of Seidel matrices with three eigenvalues and links these to bounds on equiangular lines in high-dimensional spaces.

Findings

Spectral properties of Seidel matrices up to order 13.

Classification of Seidel matrices with three eigenvalues up to order 23.

Maximum equiangular lines in R^{12} with angle 1/5 is 20.

Abstract

In this paper Seidel matrices are studied, and their spectrum and several related algebraic properties are determined for order $n\leq 13$. Based on this Seidel matrices with exactly three distinct eigenvalues of order $n\leq 23$ are classified. One consequence of the computational results is that the maximum number of equiangular lines in $\mathbb{R}^{12}$ with common angle $1/5$ is exactly $20$.