Connectivity properties of spaces of partial realizations

This paper addresses the problem of determining the number of connected com ponents of the space of real scalar M x N Hankel matrices of rank n. For n < min {M,N} it is shown that the space has n + 1 components for M + N even, and is connected for M + N odd. As an application, the number of component s of sets of minimal partial realizations of McMillan degree n less than or equal to tau of length tau sequences is determined. (C) 2001 Elsevier Scie nce B.V. All rights reserved.