NONE 20260316102800361 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON MATHEMATICS 1109-2769 2224-2880 Di̇dem Ersanli Bahti̇yar Department of Mathematics TOBB Economics and Technology University Söğütözü, 06560, Ankara TURKEY Emrah Kiliç Department of Mathematics TOBB Economics and Technology University Söğütözü, 06560, Ankara TURKEY We define a new variant of Filbert-like matrices with entries defined by ratios of terms from general Fibonacci and Lucas sequences as well as they are defined differently based on the parity of the row indices. For each matrix, we find L and U matrices related to LU-decomposition, their inverses, inverse of the each matrix, and its determinant. All results are valid for general q. The results for general Fibonacci and Lucas numbers are obtained as natural consequences for the particular selection of q. 12 31 2025 12 31 2025 766 76 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/23206.2025.24.76 https://wseas.com/journals/mathematics/2025/b545106-2312.pdf L. Carlitz, The characteristic polynomial of a certain matrix of binomial coefficients, Fibonacci Quart., 3(2) (1965), 81-89. https://doi.org/10.1080/00150517.1965. 12431433 W. Chu, Finite differences and determinant identities, Linear Algebra Appl., 430(1) (2009), 215-228. https://doi.org/10.1016/j.laa.2007.08. 044 W. Chu, Hankel determinants of factorial fractions, Bull. Aust. Math. Society, 105(1) (2022), 46-57. https://doi.org/10.1017/ S0004972721000423 A. Edelman and G. Strang, Pascal matrices, Amer. Math. Monthly, 111(3) (2004), 189-197. https://doi.org/10.1080/00029890.2004. 11920065 M. Merca, A note on the determinant of a Toeplitz-Hessenberg matrix, Spec. Matrices, 1 (2013), 10-16. https://doi.org/10.2478/ spma-2013-0003 T. M. Richardson, The Filbert matrix, (1999) arXiv preprint math/9905079. https://doi.org/10.48550/arXiv.math/ 9905079 T. Komatsu, Fibonacci determinants with Cameron’s operator, Boletín de la Sociedad Matemática Mexicana, 26(3) (2020), 841-863. https://doi.org/10.1007/ s40590-020-00286-z Y. Khiar, E. Mainar, J. M. Pena, E. RoyoAmondarain and B. Rubio, Bidiagonal Factorizations of Filbert and Lilbert Matrices, Axioms, 13(4) (2024), 219. https://doi.org/10.3390/ axioms13040219 P. Trojovský, On a sequence of tridiagonal matrices whose determinants are Fibonacci numbers, Int. J. Pure Appl. Math., 102(3) (2015), 527-532. https://doi.org/10.12732/ijpam.v102i3. 10 E. Kılıç and D. Ersanlı, A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity, Math. Slovaca, 74(3) (2024), 587- 594. https://doi.org/10.1515/ms-2024-0044