  A subspace of matrices over $\mathbb{F}_{q^e}^{m\times n}$ can be naturally
embedded as a subspace of matrices in $\mathbb{F}_q^{em\times en}$ with the
property that the rank of any of its matrix is a multiple of $e$. It is quite
natural to ask whether or not all subspaces of matrices with such a property
arise from a subspace of matrices over a larger field. In this paper we explore
this question, which corresponds to studying divisible codes in the rank
metric. We determine some cases for which this question holds true, and
describe counterexamples by constructing subspaces with this property which do
not arise from a subspace of matrices over a larger field.
