A nonlinear generalization of the Filbert matrix and its Lucas analogue

KILIÇ E., ARIKAN T.

LINEAR & MULTILINEAR ALGEBRA, vol.67, no.1, pp.141-157, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1080/03081087.2017.1412393
  • Journal Name: LINEAR & MULTILINEAR ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.141-157
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, wepresent both anewgeneralization and an analogue of the Filbert matrix F by the means of the Fibonacci and Lucas numbers whose indices are in nonlinear form lambda(i + r)(k) + mu(j + s)(m) + c for the positive integers., mu, k, m and the integers r, s, c. This will be the first example as nonlinear generalizations of the Filbert and Lilbert matrices. Furthermore, we present q-versions of these matrices and their related results. We derive explicit formulae for the inverse matrix, the LU-decomposition and the inverse matrices L-1, U-1 as well as we present the Cholesky decomposition for all matrices.