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

Didem Ersanlı; Emrah Kılıç

doi:10.15672/hujms.1264983

Research Article

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

Year 2024, Early Access, 1 - 11

Didem Ersanlı Emrah Kılıç

https://doi.org/10.15672/hujms.1264983

Abstract

In this paper, we present a new analogue of the Filbert and Lilbert matrices whose the indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formulæ are derived for the LU-decompositions, their inverses and the inverse of 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.

Keywords

Filbert matrix, Lilbert matrix, q-analogue, LU-decomposition, inverse matrix, determinant

References

[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

Year 2024, Early Access, 1 - 11

Didem Ersanlı Emrah Kılıç

https://doi.org/10.15672/hujms.1264983

Abstract

References

[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

There are 1 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Mathematics
Authors	Didem Ersanlı 0000-0002-3204-7407 Emrah Kılıç 0000-0003-0722-7382
Early Pub Date	September 14, 2023
Publication Date
Published in Issue	Year 2024 Early Access

Cite

APA	Ersanlı, D., & Kılıç, E. (2023). Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices. Hacettepe Journal of Mathematics and Statistics1-11. https://doi.org/10.15672/hujms.1264983
AMA	Ersanlı D, Kılıç E. Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices. Hacettepe Journal of Mathematics and Statistics. Published online September 1, 2023:1-11. doi:10.15672/hujms.1264983
Chicago	Ersanlı, Didem, and Emrah Kılıç. “Curious Harmony in Asymmetric & Nonlinear Variant of Filbert and Lilbert Matrices”. Hacettepe Journal of Mathematics and Statistics, September (September 2023), 1-11. https://doi.org/10.15672/hujms.1264983.
EndNote	Ersanlı D, Kılıç E (September 1, 2023) Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices. Hacettepe Journal of Mathematics and Statistics 1–11.
IEEE	D. Ersanlı and E. Kılıç, “Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices”, Hacettepe Journal of Mathematics and Statistics, pp. 1–11, September 2023, doi: 10.15672/hujms.1264983.
ISNAD	Ersanlı, Didem - Kılıç, Emrah. “Curious Harmony in Asymmetric & Nonlinear Variant of Filbert and Lilbert Matrices”. Hacettepe Journal of Mathematics and Statistics. September 2023. 1-11. https://doi.org/10.15672/hujms.1264983.
JAMA	Ersanlı D, Kılıç E. Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices. Hacettepe Journal of Mathematics and Statistics. 2023;:1–11.
MLA	Ersanlı, Didem and Emrah Kılıç. “Curious Harmony in Asymmetric & Nonlinear Variant of Filbert and Lilbert Matrices”. Hacettepe Journal of Mathematics and Statistics, 2023, pp. 1-11, doi:10.15672/hujms.1264983.
Vancouver	Ersanlı D, Kılıç E. Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices. Hacettepe Journal of Mathematics and Statistics. 2023:1-11.