Noferini, Vanni
(2015)
*When is a Hamiltonian matrix the commutator of two skew-Hamiltonian matrices?*
Linear and Multilinear Algebra, 63 (8).
pp. 1531-1552.
DOI https://doi.org/10.1080/03081087.2014.952729

Noferini, Vanni
(2015)
*When is a Hamiltonian matrix the commutator of two skew-Hamiltonian matrices?*
Linear and Multilinear Algebra, 63 (8).
pp. 1531-1552.
DOI https://doi.org/10.1080/03081087.2014.952729

Noferini, Vanni
(2015)
*When is a Hamiltonian matrix the commutator of two skew-Hamiltonian matrices?*
Linear and Multilinear Algebra, 63 (8).
pp. 1531-1552.
DOI https://doi.org/10.1080/03081087.2014.952729

## Abstract

The mapping (Formula presented.) , where the matrices (Formula presented.) are skew-Hamiltonian with respect to transposition, is studied. Let (Formula presented.) be the range of (Formula presented.) : we give an implicit characterization of (Formula presented.) , obtaining results that find an application in algebraic geometry. Namely, they are used in [R. Abuaf and A. Boralevi, Orthogonal bundles and skew-Hamiltonian matrices, Submitted] to study orthogonal vector bundles. We also give alternative and more explicit characterizations of (Formula presented.) for (Formula presented.). Moreover, we prove that for (Formula presented.) , the complement of (Formula presented.) is nowhere dense in the set of (Formula presented.) -dimensional Hamiltonian matrices, denoted by (Formula presented.) , implying that almost all matrices in (Formula presented.) are in (Formula presented.) for (Formula presented.). Finally, we show that (Formula presented.) is never surjective as a mapping from (Formula presented.) to (Formula presented.) , where (Formula presented.) is the set of (Formula presented.) -dimensional skew-Hamiltonian matrices. Along the way, we discuss the connections of this problem with several existing results in matrix theory.

Item Type: | Article |
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Uncontrolled Keywords: | Roth's theorem; orthogonal vector bundle; bow tie form; commutator; skew-Hamiltonian matrix; Hamiltonian matrix; 15B57; 15A21 |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematical Sciences, Department of |

SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |

Depositing User: | Unnamed user with email elements@essex.ac.uk |

Date Deposited: | 20 Oct 2015 13:28 |

Last Modified: | 18 Aug 2022 11:31 |

URI: | http://repository.essex.ac.uk/id/eprint/15326 |

## Available files

**Filename:** MIMS_ep2014_15.pdf