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We prove explicit lower bounds for the smallest singular value and upperbounds for the condition number of rectangular, multivariate Vandermondematrices with scattered nodes on the complex unit circle. Analogously to theShannon-Nyquist criterion, the nodes are assumed to be separated by a constantdivided by the used polynomial degree. If this constant grows linearly with thespatial dimension, the condition number is uniformly bounded. If it grows onlylogarithmically with the spatial dimension, the condition number grows slightlystronger than exponentially with the spatial dimension. Both results are quasioptimal and improve over all previously known results of such type.

Multivariate Vandermonde matrices with separated nodes on the unit circle are stable