Some Properties of the Q-adic Vandermonde Matrix Vaidyanath Mani and Robert E. Hartwig

The Vandermonde and con uent Vandermonde matrices are of fundamental signi cance in matrix theory. A further generalization of the Vandermonde matrix called the q-adic coe cient matrix was introduced in [V. Mani and R. E. Hartwig, Lin. Algebra Appl., to appear]. It was demonstrated there that the q-adic coe cient 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 coe cient 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 coe cient matrix is also explored using a modi ed de nition of the partial derivative operator.