Factorizations related to the reciprocal Pascal matrix
Helmut Prodinger
TL;DR
This paper derives explicit LU-decompositions for the reciprocal Pascal matrix and its inverse, including q-analogues, providing new formulas for these factorizations and related matrices.
Contribution
It presents the first explicit formulas for LU-decompositions of the reciprocal Pascal matrix and its inverse, along with q-analogues, advancing understanding of these special matrices.
Findings
Explicit LU-decomposition formulas derived
Formulas extended to inverse and related matrices
q-analogues of all results provided
Abstract
The reciprocal Pascal matrix has entries . Explicit formullae for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, -analogues are also presented.
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