Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences

Year 2019, Volume: 11, 65 - 71, 30.12.2019

Yasemin Taşyurdu Fikret Işık

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

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