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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries

Emrah Kılıç(TOBB University of Economics and Technology)0000-0003-0722-7382
Neşe Ömür(Kocaeli University)0000-0002-3972-9910
Sibel Koparal(Kocaeli University)0000-0001-9574-9652
Pages
—
Publication Date
2020-04-02
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries consist of the Fibonacci and Lucas numbers.
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Key Findings & Data:We shall derive explicit formulae for their $LU$-decompositions and inverses.
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Conclusion & Impact:To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized Filbert matrix · q-analogues · LU-decomposition

Abstract

In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulae for their $LU$-decompositions and inverses. To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.

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Cite This Article

Kılıç, E., Ömür, N., Koparal, S. (2020). New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.473495

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