论文标题
波西米亚矩阵几何
Bohemian Matrix Geometry
论文作者
论文摘要
波西米亚矩阵家族是一组矩阵，其所有条目都是从固定（通常是离散的，因此是界限）的特征零字段的子集中绘制的。最初，这些是整数 - 因此，来自整数的缩写高度矩阵（Bohemi）的名称 - 但其他类型的条目也很有趣。关于波西米亚矩阵的某些问题可以通过数值计算来回答，但有时精确的计算更好。在本文中，我们通过计算一些波西米亚家庭（对称，上海森堡或Toeplitz），并回答有关特征值密度分布提出的一些开放问题。
A Bohemian matrix family is a set of matrices all of whose entries are drawn from a fixed, usually discrete and hence bounded, subset of a field of characteristic zero. Originally these were integers -- hence the name, from the acronym BOunded HEight Matrix of Integers (BOHEMI) -- but other kinds of entries are also interesting. Some kinds of questions about Bohemian matrices can be answered by numerical computation, but sometimes exact computation is better. In this paper we explore some Bohemian families (symmetric, upper Hessenberg, or Toeplitz) computationally, and answer some open questions posed about the distributions of eigenvalue densities.
