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.

Keywords:

• Sylvester–Kac matrix
• determinant
• eigenvalues

2010 Mathematics Subject Classifications:

• 15A18
• 15A15

Disclosure statement

No potential conflict of interest was reported by the authors.