Abstract
In this paper we study the topology of manifolds of rectangular Hankel matrices, motivated by the problem of partial realization. Following Fischer and Frobenius, we introduce a rank-preserving Gl(2, ℝ)-action on the space Hank(M × N) of all realM × N Hankel matrices. We derive an explicit formula for the firstn x n principal minor of transformed Hankel matrices. Extending the earlier work of Brockett, the formula is applied to introduce a manifold structure on the space Hank(n, M × N) of allM × N Hankels of rankn. We construct a cell decomposition of Hank(M × N) which induces a cellular subdivision on each of the manifolds Hank(n, M × N) wheren ≤ min (M, N). This new cell decomposition is applied to investigate the topology of partial realizations.
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Manthey, W., Helmke, U. & Hinrichsen, D. Topological aspects of the partial realization problem. Math. Control Signal Systems 5, 117–149 (1992). https://doi.org/10.1007/BF01215842
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DOI: https://doi.org/10.1007/BF01215842