Mackey, D. Steven and Mackey, Niloufer and Mehl, Christian and Mehrmann, Volker
(2009)
*Jordan Structures of Alternating Matrix Polynomials.*
[MIMS Preprint]

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## Abstract

Alternating matrix polynomials, that is, polynomials whose coecients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. We investigate the Smith forms of alternating matrix polynomials, showing that each invariant factor is an even or odd scalar polynomial. Necessary and sucient conditions are derived for a given Smith form to be that of an alternating matrix polynomial. These conditions allow a characterization of the possible Jordan structures of alternating matrix polynomials, and also lead to necessary and sucient conditions for the existence of structure-preserving strong linearizations. Most of the results are applicable to singular as well as regular matrix polynomials.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | matrix polynomial, matrix pencil, structured linearization, Smith form, Jordan form, elementary divisor, invariant factor, invariant polynomial, alternating matrix polynomial, even/odd matrix polynomial. |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 03 Oct 2009 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1314 |

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