A note on Bernstein-Vandermonde matrices

Abstract

ABSTRACTThe inverse matrix of a Vandermonde matrix with arbitrary field entries of dimension with is well-studied in the literature. Especially, an explicit inversion formula does exist. However in theory as e.g. for determining (analytically) the eigenvalues of (arbitrary) matrix polynomials, Bernstein-Vandermonde matrices must be inverted. This note derives an explicit low-cost inversion formula for this matrix class with entries over a field whose characteristic equals zero. Its derivation requires at most additions and multiplications.