Dopico, Froilan M. and Noferini, Vanni
*Root polynomials and their role in the theory of matrix polynomials.*
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## Abstract

We give a coherent theory of root polynomials, an algebraic tool useful for the analysis of matrix polynomials. In particular, we first survey results previously appeared in the literature, giving a formal proof for those that lacked one. We next extend some of these results providing some new concepts and related theorems, thus simplifying and expanding the theory. Then, we give some applications of root polynomials, such as the recovery of Jordan chains from linearizations of matrix polynomials, or the behaviour of Jordan chains under rational reparametrization. We also briefly discuss how root polynomials can be used to define eigenvectors and eigenspaces for singular matrix polynomials.

Item Type: | Article |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory |

Depositing User: | Dr V Noferini |

Date Deposited: | 23 Sep 2018 04:43 |

Last Modified: | 23 Sep 2018 13:53 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2659 |

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