- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 2
- New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries
New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries
Authors : Emrah Kiliç, Neşe Ömür, Sibel Koparal
Pages : 684-694
Doi:10.15672/hujms.473495
View : 10 | Download : 3
Publication Date : 2020-04-02
Article Type : Research
Abstract :In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulae for their $LU$-decompositions and inverses. To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.Keywords : Generalized Filbert matrix, q-analogues, LU-decomposition, Zeilberger’s algorithm, Computer algebra system (CAS)