On the parametrization of the controllability subspaces of a controllable pair
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Given a controllable linear control system defined by a pair of constant matrices (A;B), the set of controllability subspaces is an stratified submanifold of the set of (A;B)-invariant subspaces. We parameterize each strata by means of coordinate charts. This parametrization has significant di®erences to that of (A;B) invariant subspaces, showing a more complex geometric structure.