Conditioned Invariant Subspaces and the Geometry of Nilpotent Matrices

Matrices with eigenvectors in a given subspace

“…The irreducibility and dimension part of Proposition 1.2 was proved in the 1983 PhD dissertation of Uwe Helmke, where he used it to compute the homotopy groups of the space of controllable pairs (A, C). The desingularization technique of our Section 4 is close to [7], where the approach was to look at the moment map in the setting of symplectic geometry. A point of view related to ours is also found in [3].…”