In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of numbers. We examine some identities quaternions. introduce their basic definitions and properties. give Binet’s formula, Cassini’s identity, Catalan’s d’Ocagne generating functions, exponential functions also relations between Jacobsthal

A variation of the Filbert matrix from [1] is introduced, which has one additional Fibonacci factor in the numerator. We also introduce its Lucas counterpart by taking Lucas numbers instead of Fibonacci numbers in a similar manner. Explicit formulæ are derived for the LU-decompositions, their inverses, the inverse matrix, as well as the Cholesky decompositions. The approach is to use q-analysis...