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.

翻译：波希米亚矩阵组是一组矩阵,其所有条目都来自一个固定的、通常互不关联的、因此相互连接的、零特性域的子集。最初这些是整数 -- -- 因此是首字母,取自首字母缩略词 " BOHEMI " (BOHEMI) -- -- 但其他种类的条目也很有意思。关于波希米亚矩阵的一些问题可以通过数字计算解答,但有时精确的计算更好。在本文件中,我们用计算方式探索一些波希米亚家族(对称、上赫森贝格或托普利茨),并回答一些关于电子值密度分布的公开问题。