An explicit formula for the inverse of a factorial Hankel matrix
arXiv:1808.028803 citationsh-index: 4
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Provides a theoretical result for linear algebra and combinatorial matrix theory, but is incremental as it solves a specific matrix structure.
The paper derives an explicit formula for the inverse of a factorial Hankel matrix, proving its invertibility for all n.
We consider the $n\times n$ Hankel matrix $H$ whose entries are defined by $H_{ij}=1/s_{i+j}$ where $s_k=(k-1)!$ and prove that $H$ is invertible for all $n\in\mathbb{N}$ by providing an explicit formula for its inverse matrix.