Geometric characterization and classification of marked subspaces Original Research Article

Given an endomorphism of a finite dimensional image-vector space, we obtain geometric conditions in order to characterize and to classify the marked invariant subspaces W subset of E (that is to say, the invariant subspaces having some Jordan basis which can be extended to a Jordan basis of E). Both conditions are expressed in terms of the double family of subspaces (Ker fh ∩ Im fd). The starting point is a new criterion for extensibility of Jordan bases.