Matricial realizations of the solutions of the Carlson problem

Geometric classification of monogenic subspaces and uniparametric linear control systems

“…If f is a nilpotent endomorphism, the Weyr characteristic The geometric proof of Theorem 2.5 in [3] gives an explicit computation of the LR-sequence for an invariant subspace which we recall in Lemma 2.7. The construction for the converse (II) ⇒ (I) will be used in the next section.…”

“…We recall that the "Carlson condensation Lemma" (see for example [3]) ensures that any global characteristic α can be obtained by means of a suitable matrix A ′ 3 of this kind provided that α is compatible with γ, β. We recall also that given α, γ, then β classifies the monogenic subspaces.…”

Miniversal deformations of observable marked matrices

“…For instance, in , one proves that the ‘simplest’ solutions of the Carlson problem are marked, and any other solution appears in a neighborhood of the marked ones. This notion was extended to pairs of matrices in and used in for the analog to the Carlson problem: Again, the marked solutions cover all the possibilities and are the simplest realizations. Moreover, from the versal deformation of a pair in , it follows that ‘minimal’ observable perturbations of a nonobservable pair are marked.…”

“…So, in , the perturbation of a square matrix preserving an invariant subspace is studied. In particular, this perturbation gives all the solutions of the Carlson problem, and hence, explicit realizations can be obtained (see ).…”

Perturbations preserving conditioned invariant subspaces

“…So, in , the perturbation of a square matrix preserving an invariant subspace is studied. In particular, this perturbation gives all the solutions of the Carlson problem, and hence explicit realizations can be obtained .…”