A rank theorem for Vandermonde matrices is discussed. It is shown that certain matrices built from Vandermonde matrices are of full rank. It is observed that this result plays a key role in the 'limit theory of generic polynomials'. An alternative proof for a particular theorem based on methods from the theory of linear recurrences is given.
Koiran, P., Portier, N., & Villard, G. (2004). A rank theorem for Vandermonde matrices. Linear Algebra and Its Applications, 378(1–3), 99–107. https://doi.org/10.1016/j.laa.2003.09.007