On the singularity of generalised Vandermonde matrices over finite fields

We use an upper bound on the number of zeros of sparse polynomials over a finite field Fq to estimate the number of singular matrices of the form (λiuj)i,j=1m, where λ1,…,λm∈Fq* are fixed nonzero elements, taken over all (q-1)m integer m-tuples (u1,…,um)∈[0,q-2]m.