The spectrum of a new class of Sylvester-Kac matrices

Abstract

We define a new class of Sylvester-Kac matrices and calculate its spectrum
explicitly. We use the technique of the left eigenvalues to obtain the claim.
We also provide the right eigenvalues which can be useful in applied
computations. The main results are rather general and contain many known
particular characterizations. This family of tridiagonal matrices is a
convenient test matrix for numerical eigenvalue computations with known spectrum.