A. Alazemi, C.M. da Fonseca, E. Kılıç (2021) The spectrum of a new class of Sylvester-Kac matrices, Filomat, Vol. 35, pp.4017-4031, 10.2298/FIL2112017A
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.