Given a pair of matrices representing a controllable linear system, its equivalence
classes by the single or combined action of feedbacks, change of state and input variables, as well as
their intersection are studied. In particular, it is proved that they are differentiable manifolds and
their dimensions are computed. Some remarks concerning the effect of different kinds of feedbacks
Compta, A.; Ferrer, J.; Peña, M. Geometric structure of single/combined equivalence classes of a controllable pair. "Electronic journal of linear algebra", Novembre 2011, vol. 22, p. 1112-1128.