The Vandermonde Matrix in the Commutative Case

A. I. Perov^a^,*, and I. D. Kostrub^a^,**

^aVoronezh State University, Voronezh, Russia

email: *anperov@mail.ru
email: **ikostrub@yandex.ru

Received 24 December, 2023

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

DOI: 10.1134/S1064562424702041