Nonlinear variants of the generalized Filbert and Lilbert matrices

Authors

EMRAH KILIÇ
SİBEL KOPARAL
NEŞE ÖMÜR

Abstract

In this paper, we present variants of the generalized Filbert and Lilbert matrices by products of the general Fibonacci and Lucas numbers whose indices are in certain nonlinear forms of the indices with certain integer parameters. We derive explicit formulæ for inverse matrix, LU -decomposition and inverse matrices $L^{-1}$ and $U^{-1}$ for all matrices. Generally, we present $q$-versions of these matrices and their related results.

DOI

10.3906/mat-1909-62

Keywords

Filbert and Lilbert matrices, inverse matrix determinant, generalized Pochhammer symbol, Fibonacci and Lucas numbers

First Page

622

Last Page

642

Recommended Citation

KILIÇ, EMRAH; KOPARAL, SİBEL; and ÖMÜR, NEŞE (2020) "Nonlinear variants of the generalized Filbert and Lilbert matrices," Turkish Journal of Mathematics: Vol. 44: No. 3, Article 1. https://doi.org/10.3906/mat-1909-62
Available at: https://journals.tubitak.gov.tr/math/vol44/iss3/1