- Turkish Journal of Mathematics and Computer Science
- Vol: 11 Special Issue
- Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences
Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences
Authors : Yasemin Taşyurdu, Fikret Işik
Pages : 65-71
View : 6 | Download : 3
Publication Date : 2019-12-30
Article Type : Other
Abstract :In this paper, we consider Hessenberg matrices and Fibonacci-Like sequences that is defined by the recurrence relation $T_{n}=T_{n-1}+T_{n-2}$, $% n\geq 2$ and $T_{0}=m$, $T_{1}=m$ where $m$ is a fixed positive integer. We define two $n\times n$ Hessenberg matrices with applications to the Fibonacci-Like sequences and investigate the determinantal and permanental properties. We obtain that the determinants and permanents of these Hessenberg matrices are equal to the $n$th term of Fibonacci-Like sequences.Keywords : Fibonacci sequence, Lucas sequence, Determinant, Permanent, Hessenberg matrix