Vaidyanath Mani and Robert E. Hartwig, Some properties of the q-adic Vandermonde matrix, pp. 18-33

ELA, Volume 1, pp. 18-33, abstract.

Some Properties of the q-adic Vandermonde Matrix

Vaidyanath Mani and Robert E. Hartwig


The Vandermonde and confluent Vandermonde matrices are of fundamental
significance in matrix theory. A further generalization of the
Vandermonde matrix called the q-adic coefficient matrix was
introduced in [V. Mani and R. E. Hartwig, Lin. Algebra Appl., to appear].
It was demonstrated there that the q-adic coefficient matrix reduces the
Bezout matrix of two polynomials by congruence. This extended the work
of Chen, Fuhrman, and Sansigre among others. In this paper, some
important properties of the $q$-adic  coefficient matrix are studied.
It is shown that the determinant of this matrix is a product of
resultants (like the Vandermonde matrix). The Wronskian-like block
structure of the q-adic coefficient matrix is also explored
using  a modified definition of the partial derivative operator.