论文标题
在间隔[-2,2]
Symmetrizable integer matrices having all their eigenvalues in the interval [-2,2]
论文作者
论文摘要
图的邻接矩阵形成了所有整数对称矩阵集的特殊子集。哪个图的描述在[-2,2]（即最多具有光谱半径2）的间隔中具有所有特征值已知数十年。在2007年，我们将此分类扩展到任意整数对称矩阵。 在本文中，我们将注意力转向了同样的矩阵。我们将连接的非对称但对称的矩阵进行分类，这些矩阵在$ \ z $中的条目相对于在[-2,2]中具有所有特征值的最大值。这包括仿射和有限的Dynkin图的光谱表征，这些图并不简单地绑扎（图形结果给出了简单绑带的频谱表征）。
The adjacency matrices of graphs form a special subset of the set of all integer symmetric matrices. The description of which graphs have all their eigenvalues in the interval [-2,2] (i.e., those having spectral radius at most 2) has been known for several decades. In 2007 we extended this classification to arbitrary integer symmetric matrices. In this paper we turn our attention to symmetrizable matrices. We classify the connected nonsymmetric but symmetrizable matrices which have entries in $\Z$ that are maximal with respect to having all their eigenvalues in [-2,2]. This includes a spectral characterisation of the affine and finite Dynkin diagrams that are not simply laced (much as the graph result gives a spectral characterisation of the simply laced ones).
