The largest entry in the inverse of a Vandermonde matrix. Issue 20 (19th December 2022)

• Record Type: Journal Article
• Authors: Sanna, Carlo; Shallit, Jeffrey; Zhang, Shun
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 20(2022)
• Page Start: 5634
• Page End: 5641
• Publication Date: 2022-12-19
• Subjects: S. Friedland; Vandermonde matrix -- inverse; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1922337
• Languages: English
• ISSNs: 0308-1087

Abstract

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 × 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.