The q-Pilbert matrix

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

2000 AMS Subject Classification :

• 11B39

Acknowledgements

Thanks are due to two referees who spotted small inaccuracies and made suggestions towards a better presentation.

Additional information

Notes on contributors

Helmut Prodinger

This author was supported by an incentive grant from the NRF of South Africa.