In this paper, we discuss maximality of Seidel matrices with a fixed largest eigenvalue. We present a classification of maximal Seidel matrices of largest eigenvalue 3, which gives a classification of maximal equiangular lines in a Euclidean space with angle \(\arccos 1/3\). Motivated by the maximality of the exceptional root system \(E_8\), we define strong maximality of a Seidel matrix, and show that every Seidel matrix achieving the absolute bound is strongly maximal.

中文翻译：

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Seidel 矩阵的极大值和图的切换根

在本文中，我们讨论具有固定最大特征值的 Seidel 矩阵的极大值。我们提出了最大特征值 3 的最大赛德尔矩阵的分类，它给出了角为\(\arccos 1/3\)的欧几里得空间中的最大等角线的分类。受异常根系统\(E_8\)极大值的启发，我们定义了一个 Seidel 矩阵的强极大值，并证明每个达到绝对边界的 Seidel 矩阵都是强极大值。