The possible observability indices of an observable pair of matrices, when supplementary subpairs are prescribed, are characterized when the “quotient” one is nilpotent. The geometric techniques used are also valid in the ...

The classification of the invariant subspaces of an endomorphism has been an open problem for a long time, and it is a ”wild” problem in the general case. Here we obtain a full classification for the monogenic ones. Some ...

Mitjançant tècniques geomètriques, abordem les qüestions següents:<br/><br/>(i) Estudi (caracterització, classificació, famílies diferenciables,...) d'una classe destacada de subespais invariants, els anomenats ...

We present a geometric approach to the classification of monogenic invariant subspaces, alternative to the classical algebraic one, which allows us to obtain several matricial canonical forms for each class. Some applications ...

Given a pair of matrices representing a controllable linear system, we study its equivalence classes by the single or combined action of feedbacks and change of state and input variables, as well as their intersections. ...

The Klein theorem asserts the existence of a solution of the Carlson problem when a related Littelewood-Richardson sequence exists. Here we present an explicit construction of these matricial solutions.

Given the set of vertical pairs of matrices ${\cal M}\subset M_{m,n}(\mathbb C)\times M_n(\mathbb C)$ keeping the subspace $\mathbb C^d\times\{0\}\subset\mathbb C^n$ invariant,we compute miniversal deformations of a given ...

Given S an (A;B)-invariant subspace, we prove that the set of friend feedbacks is a (nm¡md+dq)-dimensional linear variety, which can be considered as the direct sum of the feedbacks of the restriction to S and the ...