A new type of Sylvester–Kac matrix and its spectrum

Abstract

The Sylvester–Kac matrix, sometimes known as Clement matrix, has many extensions and applications throughout more than a century of its existence. The computation of the eigenvalues or even the determinant have always been challenging problems. In this paper, we aim the introduction of a new family of a Sylvester–Kac type matrix and evaluate the corresponding spectrum. As a consequence, we establish a formula for the determinant. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.