Stratification and bundle structure of the set of general (A,B)-invariant subspaces

Abstract

Given (A,B) in Hom(C^(n+m) C^n), we prove that the set of (A,B)-invariant subspaces having a fixed Brunovsky-Kronecker structure is a submanifold of the corresponding grassman manifold, and we compute its dimension. Also, we prove that the set of all (A,B)-invariant subspaces having a fixed dimension is connected, provided that (A,B) has only one eigenvalue.