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The q-Pilbert matrix |
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| Abstract: | A generalized Filbert matrix is introduced, sharing properties of the Hilbert matrix and Fibonacci numbers. Explicit formulae are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger's celebrated algorithm. |
| Keywords: | Filbert matrix Fibonacci numbers q-analogues LU-decomposition Cholesky decomposition Zeilberger's algorithm |