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Dergiler / 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
Sayfa
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Yayın Tarihi
2024-06-27
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:Explicit formulae are derived for the $LU$-decompositions, their inverses and the inverse of the main matrix as well as its determinant.
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Sonuç & Katkı:The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular $q$ value.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (15)

  1. Y. Amanbek, Z. Du, Y. Erlangga, C.M. da Fonseca, B. Kurmanbek and A. Pereira, Explicit determinantal formula for a class of banded matrices, Open Math. 18 (1), 1227-1229, 2020.
  2. M. Andelic and C.M. da Fonseca, Some determinantal considerations for pentadiagonal matrices, Linear Multilinear Algebra 69 (16), 3121-3129, 2021.
  3. J.E. Anderson and C. Berg, Quantum Hilbert matrices and orthogonal polynomials, J. Comput. Appl. Math. 223 (3), 723-729, 2009.
  4. T. Arıkan, E. Kılıç and H. Prodinger, A nonsymmetrical matrix and its factorizations, Math. Slovaca 69 (4), 753-762, 2019.
  5. L. Carlitz, The characteristic polynomial of a certain matrix of binomial coefficients, Fibonacci Q. 3, 81-89, 1965.
  6. W. Chu and L. Claudio, Binomial determinant evaluations, Ann. Comb. 9 (4), 363- 377, 2005.
  7. W. Chu, Finite differences and determinant identities, Linear Algebra Appl. 430, 215-228, 2009.
  8. A. Edelman and G. Strang, Pascal matrices, Am. Math. Mon. 111, 189-197, 2004.
  9. E. Kılıç and T. Arıkan, A class of non-symmetric band determinants with the Gaussian q-binomial coefficients, Quaest. Math. 40 (5), 645-660, 2017.
  10. E. Kılıç and T. Arıkan, A nonlinear generalization of the Filbert matrix and its Lucas analogue, Linear Multilinear Algebra 67, 141-157, 2019.
  11. E. Kılıç and D. Ersanlı, Harmony of asymmetric variants of the Filbert and Lilbert matrices in q-form, Math. Slovaca 73 (3), 633-642, 2023.
  12. E. Kılıç, N. Ömür and S. Koparal, Nonlinear variants of the generalized Filbert and Lilbert matrices, Turk. J. Math. 44, 622-642, 2020.
  13. E. Kılıç and H. Prodinger, Asymmetric generalizations of the Filbert matrix and variants, Publ. de l’Institut Math. (Beograd) (NS) 95 (109), 267-280, 2014.
  14. M. Merca, A note on the determinant of a Toeplitz-Hessenberg matrix, Spec. Matrices 1, 10-16, 2013.
  15. T. Richardson, The Filbert matrix, Fibonacci Q. 39 (3), 268-275, 2001.