Nonlinear variants of the generalized Filbert and Lilbert matrices

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.