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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 53 Issue: 3

Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices

Emrah Kılıç(TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGY)0000-0003-0722-7382
Didem Ersanlı(TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGY)0000-0002-3204-7407
Pages
—
Publication Date
2024-06-27
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AI Summary & Key Takeaways

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

The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular $q$ value.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we present a new analogue of the Filbert and Lilbert matrices whose indices have different asymmetric and nonlinear rules according to their row numbers.
📊
Key Findings & Data:Explicit formulae are derived for the $LU$-decompositions, their inverses and the inverse of the main matrix as well as its determinant.
💡
Conclusion & Impact:The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular $q$ value.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Filbert matrix · Lilbert matrix · q-analogue

Abstract

In this paper, we present a new analogue of the Filbert and Lilbert matrices whose indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formulae are derived for the $LU$-decompositions, their inverses and the inverse of the main matrix as well as its determinant. To prove the claimed results we use backward induction method. The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular $q$ value.

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Cite This Article

Kılıç, E., Ersanlı, D. (2024). Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 3. https://doi.org/10.15672/hujms.1264983

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