Harmony of Asymmetric Variants of the Filbert and Lilbert Matrices in q-form

Abstract

We define a new matrix whose entries are defined by the idea of combining two different asymmetric rules. We will derive explicit formulæ for the matrices L and U come from LU-decomposition, L-1, U-1, inverse of the main matrix as well as its determinant. To prove the claimed results, we use backward induction method. © 2023 Mathematical Institute Slovak Academy of Sciences.