Realization of rational matrices by singular systems

We study the relationship between spaces of singular systems and rational matrices. In a recent paper it is shown that the space of all rational p×m-matrices of fixed McMillan degree r is embedded in a space of rational curves of degree r from the Riemann sphere S² to a Grassmannian manifold. This space of curves is locally homeomorphic to the space of all proper rational matrices of degree r. In this paper we study the space of square irreducible (not necessarily admissible) singular systems. It is shown that the space of these systems of order r and dimension r+min{m, p} modulo strong equivalence is homeomorphic to the above mentioned space of all rational curves of degree r. The homeomorphism is induced by the transfer matrix.