Kılıç, Emrah; Prodinger, Helmut Variants of the Filbert matrix. (English) Zbl 1306.11019 Fibonacci Q. 51, No. 2, 153-162 (2013). Summary: A variation of the Filbert matrix from the authors’ paper [Fibonacci Q. 48, No. 1, 29–33 (2010; Zbl 1219.11028)] 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 formulas are derived for the LU-decompositions, their inverses, the inverse matrix, as well as the Cholesky decompositions. The approach is to use \(q\)-analysis and to guess the relevant quantities, and proving them later by induction. Cited in 1 ReviewCited in 9 Documents MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 05A30 \(q\)-calculus and related topics 15A23 Factorization of matrices Citations:Zbl 1219.11028 PDFBibTeX XMLCite \textit{E. Kılıç} and \textit{H. Prodinger}, Fibonacci Q. 51, No. 2, 153--162 (2013; Zbl 1306.11019) Full Text: Link