  We show that $\mathfrak{aff}(n)$, the Lie algebra of affine transformations
of ${\mathbb R}^n,$ is formally and analytically nondegenerate in the sense of
A. Weinstein. This means that every analytic (resp., formal) Poisson structure
vanishing at a point with a linear part corresponding to $\mathfrak{aff}(n)$ is
locally analytically (resp., formally) linearizable.
