The Spectrum of a New Class of Sylvester-Kac Matrices

Abstract

We define a new class of Sylvester-Kac matrices and calculate their spectra explicitly. We use the technique of the left eigenvectors to obtain the claim. We also provide some right eigenvectors which can be useful in applied computations. The main results are rather general and contain many known particular characterizations. Matrices belonging to this family represent a convenient test matrices for numerical eigenvalue computations with known spectrum.