Displacement structures and fast inversion formulas for q-adic Vandermonde-like matrices

A new class of so-called q-adic Vandermonde-like matrices over an arbitrary nonalgebraically closed field is introduced. This class generalizes the ordinary Vandermonde-like matrices over the complex field. Three kinds of displacement structures and fast inversion formulas for this class of matrices are presented by using displacement structure theory method, which generalize some of the well-known results for confluent Vandermonde-like matrices in the closed field case.