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Journals / Turkish Journal of Mathematics and Computer Science / 2019 / Cilt: 11 - Sayı: -

Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences

Fikret IŞIK
Yasemin Taşyurdu
Pages
65–71
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We obtain that the determinants and permanents of these Hessenberg matrices are equal tothe nth term of Fibonacci-Like sequences.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we consider Hessenberg matrices and Fibonacci-Like sequences that is defined by therecurrence relation Tn = Tn−1 + Tn−2, n ≥ 2 and T0 = m, T1 = m where m is a fixed positive integer.
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Key Findings & Data:We define twon × n Hessenberg matrices with applications to the Fibonacci-Like sequences and investigate the determinantal andpermanental properties.
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Conclusion & Impact:We obtain that the determinants and permanents of these Hessenberg matrices are equal tothe nth term of Fibonacci-Like sequences.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we consider Hessenberg matrices and Fibonacci-Like sequences that is defined by therecurrence relation Tn = Tn−1 + Tn−2, n ≥ 2 and T0 = m, T1 = m where m is a fixed positive integer. We define twon × n Hessenberg matrices with applications to the Fibonacci-Like sequences and investigate the determinantal andpermanental properties. We obtain that the determinants and permanents of these Hessenberg matrices are equal tothe nth term of Fibonacci-Like sequences.

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Cite This Article

IŞIK, F., Taşyurdu, Y. (2022). Determinants and Permanents of Hessenberg Matrices with Fibonacci-Like Sequences. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: -, 65–71. https://ajindex.com/articles/609125

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