Summary
In Gauger and Byrnes [10], a characterization of the similarity of two n ×n matrices in terms of rank conditions was given. This avoids the use of companion or Jordan canonical forms and yields effective decidability criteria for similarity. In this paper, we generalize this result to an explicit characterization when two polynomial models are isomorphic. As a corollary, we derive necessary and sufficient rank conditions for strict equivalence of arbitrary matrix pencils. We also briefly discuss the related equivalence problem for group representations. The techniques we use are based on the tensor products of polynomial models and related characterizations of intertwining maps.
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Fuhrmann, P.A., Helmke, U. (2010). Unimodular Equivalence of Polynomial Matrices. In: Hu, X., Jonsson, U., Wahlberg, B., Ghosh, B. (eds) Three Decades of Progress in Control Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11278-2_12
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DOI: https://doi.org/10.1007/978-3-642-11278-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11277-5
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