Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix

Abstract

In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the explicit formulas for its determinant and inverse.

Keywords

• sylvester-kac matrix
• fibonacci number
• characteristic polynomial
• determinant
• inverse
• 15a09
• 15a15
• 15a18