Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix-Reference-Cited by-同舟云学术

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

Published:2021-08-23 Issue:1 Volume:10 Page:40-46
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Jiang Zhaolin¹,Zheng Yanpeng²,Li Tianzi¹

Affiliation:

1. School of Mathematics and Statistics , Linyi University , Linyi 276000 , China

2. School of Automation and Electrical Engineering , Linyi University , Linyi 276000 , China

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2021-0145/pdf

Reference18 articles.

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3. [3] W.C. Chu, Fibonacci polynomials and Sylvester determinant of tridiagonal matrix, Appl. Math. Comput. 216(3) (2010), 1018-1023.

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5. [5] C.M. da Fonseca, E. Kılıç, An observation on the determinant of a Sylvester-Kac type matrix, An. Stiinţ, Univ. “Ovidius” Constan ta Ser. Mat. 28 (2020), 111-115.

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