GEOMETRIC CHARACTERIZATION AND CLASSIFICATION OF MARKED SUBSPACES

Given an endomorphism of a finite dimensional C-vector space, we obtai n geometric conditions in order to characterize and to classify the ma rked invariant subspaces W subset of E (that is to say, the invariant subspaces having some Jordan basis which can be extended to a Jordan b asis of E). Both conditions are expressed in terms of the double famil y of subspaces (Ker f(h) boolean AND Im f(d)). The starting point is c riterion for extensibility of Jordan bases.