Equivalence transformations of rational matrices and applications

The known theories of transformations between polynomial matrices are extended to the case of rational matrices. Specifically, Ω-equivalence between rational matrices having possibly different dimensions is defined, and this has the property of preserving the zero structure of rational matrices in the region Ω ⊆ C ∪ {∞}Some implications of this new equivalence transformation for linear system theory are also provided.

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