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

Year 2024, Volume: 53 Issue: 3, 724 - 734, 27.06.2024

Emrah Kılıç , Didem Ersanlı

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

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.

Keywords

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

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