Displacement structure approach to q-adic polynomial-Vandermonde and related matrices

In the present paper a new class of the so-called q-adic polynomial-Vandermonde-like matrices over an arbitrary non-algebraically closed field is introduced. This class generalizes both the simple and the confluent polynomial-Vandermonde-like matrices over the complex field, and the q-adic Vandermonde and the q-adic Chebyshev–Vandermonde-like matrices studied earlier by different authors. Three kinds of displacement structures and two kinds of fast inversion formulas are obtained for this class of matrices by using displacement structure matrix method, which generalize the corresponding results of the polynomial-Vandermonde-like and the q-adic Vandermonde-like matrices.