The generalized q-Pilbert matrix
Emrah Kılıç, Helmut Prodinger · Mathematica Slovaca · 2014
Abstract A generalized q-Pilbert matrix from[KILIÇ, E.-PRODINGER, H.: The q-Pilbert matrix, Int. J. Comput. Math. 89 (2012), 1370–1377] is further generalized, introducing one additional parameter. Explicit formulæ 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. However, the necessary identities have appeared already in disguised form in the paper referred above, so that no new computations are necessary.