Bohemian Matrix Geometry
Channel: Robert M. Corless
Date: 2022-04-14

A practice/backup talk for the Joint Lab Meeting of the Ontario Research Center for Computer Algebra to be held April 22, 2022.  I show some examples of density plots of eigenvalues of Bohemian matrices, and I give the ideas in the proofs explaining some of the behaviour we see.  In particular, I sketch the proofs using the Bendixon--Bromwitch--Hirsch theorem and the Schmidt--Spitzer theorem that explain some features of the complex symmetric case and the Unit Upper Hessenberg Toeplitz case.  The paper can be found at https://arxiv.org/abs/2202.07769 and the supporting materials can be found at https://github.com/rcorless/Bohemian-Matrix-Geometry .