  Given a complex vector subspace $V$ of $\mathbb{C}^n$, the dimension of the
amoeba of $V \cap (\mathbb{C}^*)^n$ depends only on the matroid that $V$
defines on the ground set $\{1,\ldots,n\}$. Here we prove that this dimension
is given by the minimum of a certain function over all partitions of the ground
set, as previously conjectured by Rau. We also prove that this formula can be
evaluated in polynomial time.
