The Largest Entry in the Inverse of a Vandermonde Matrix

08/03/2020

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by   Carlo Sanna, et al.

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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 × n matrix [b^i j]_0 ≤ i, j < n. We prove that lim_n → +∞ M_b(n) exists, and we provide some formulas for it.