## 2009.56: Jordan Structures of Alternating Matrix Polynomials

2009.56:
D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann
(2009)
*Jordan Structures of Alternating Matrix Polynomials.*

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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 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2009.56 |

Deposited By: | Ms Lucy van Russelt |

Deposited On: | 03 October 2009 |

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