Bohemian Matrices

Welcome to the Bohemian matrices homepage. Our website is still cooking but in the mean time you should check out our awesome gallery of Bohemian eigenvalue plots!

What are Bohemian Matrices?

A family of Bohemian matrices is a distribution of random matrices where the matrix entries are sampled from a discrete set of bounded height. The discrete set must be independent of the dimension of the matrices.

What are Bohemian Eigenvalues?

Bohemian eigenvalues are the eigenvalues of a family of Bohemian matrices.

The Characteristic Polynomial Database (CPDB)

The Characteristic Polynomial Database contains the sets of characteristic polynomials of several families of Bohemian matrices. Many properties of these families are archived in the characteristic polynomial database. Currently the database stores 1,762,728,065 characteristic polynomials from 2,366,960,967,336 matrices.

Why “Bohemian”?

When this project was in its early stages, our focus was on random integer matrices of bounded height. We originally used the phrase “bounded height integer matrix eigenvalues” to refer to our work. This led to the acronym BHIME which isn’t to far off from “Bohemian”.


If you are interested in learning more about Bohemian matrices, feel free to contact Steven Thornton at, or Rob Corless at

Details about our research group can be found at Ontario Research Centre for Computer Algebra (ORCCA).