This article is cited in 1 paper

MATHEMATICS

The Vandermonde matrix in the commutative case

A. I. Perov, I. D. Kostrub

Voronezh State University, Voronezh, Russian Federation

Abstract: In a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde matrix are formulated and proved. Necessary and sufficient conditions for the invertibility of the Vandermonde matrix are given. Analogues of Sylvester’s theorem are formulated.

Keywords: commutative Banach algebra, Vandermonde matrix, Sylvester's theorem, spectrum mapping theorem.

UDC: 517.957

Presented: V. V. Kozlov
Received: 24.12.2023
Revised: 04.05.2024
Accepted: 12.05.2024

DOI: 10.31857/S2686954324030057

 English version: Doklady Mathematics, 2024, 109:3, 216–220

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