A Hankel Determinant Evaluation: An Asymmetric and Nonlinear Variant of Filbert-like Matrices

Source abstract

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.