Special Matrices (Aug 2021)

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

  • Jiang Zhaolin,
  • Zheng Yanpeng,
  • Li Tianzi

DOI
https://doi.org/10.1515/spma-2021-0145
Journal volume & issue
Vol. 10, no. 1
pp. 40 – 46

Abstract

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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