2023/11/18 by Nicholas M. Ercolani, Ercolani, Nicholas, John Peca-Medlin +3
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Topics in Algebra #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2311.10978
In this paper we define and lay the groundwork for studying a novel matrix ensemble: totally positive Hessenberg Toeplitz operators, denoted TPHT. This is the intersection of two ensembles that have been significantly explored: totally positive Hessenberg matrices (TPH) and Hessenberg Toeplitz matrices (HT). TPHT has a rich linear algebraic and spectral structure that we describe. Along the way we find some previously unnoticed connections between certain Toeplitz normal forms for matrices and Lie theoretic interpretations. We also numerically study the spectral asymptotics of TPH matrices via the TPHT ensemble and use this to open a study of TPHT with random symbols.