Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences

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.