Bohemian Matrix Geometry

Abstract

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.

arXiv comment22 pages; 12 figures

References in corpus (4)

• Level-Spacing Distributions and the Airy Kernel
• Optimizing colormaps with consideration for color vision deficiency to enable accurate interpretation of scientific data
• Eigenvalues of even very nice Toeplitz matrices can be unexpectedly erratic
• The Eigenvalues of Tridiagonal Sign Matrices are Dense in the Spectra of Periodic Tridiagonal Sign Operators