Abstract
The spectral properties of n×n matrix polynomials are studied in terms of their (isospectral) linearizations. The main results in this paper concern the parametrization of strict equivalence and congruence transformations of the linearizations. The “centralizer” of the appropriate Jordan canonical form plays a major role in these parametrizations. The transformations involved are strict equivalence or congruence according as the polynomials in question have no symmetry, or are Hermitian, respectively. Jordan structures over either the complex numbers or the real numbers are used, as appropriate.
Mathematics Subject Classification (2000). 15A21, 15A54, 47B15
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Lancaster, P., Zaballa, I. (2012). Parametrizing Structure Preserving Transformations of Matrix Polynomials. In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_18
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DOI: https://doi.org/10.1007/978-3-0348-0221-5_18
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