The Largest Entry in the Inverse of a Vandermonde Matrix

Carlo Sanna; Jeffrey Shallit; Shun Zhang

paper

The Largest Entry in the Inverse of a Vandermonde Matrix

arXiv:2008.01012

Abstract

We investigate the size of the largest entry (in absolute value) in the inverse of certain Vandermonde matrices. More precisely, for every real $b > 1$ , let $M_{b} (n)$ be the maximum of the absolute values of the entries of the inverse of the $n \times n$ matrix $[b^{ij}]_{0 \leq i, j < n}$ . We prove that $lim_{n \to + \infty} M_{b} (n)$ exists, and we provide some formulas for it.