Noferini, V (2015) 'When is a Hamiltonian matrix the commutator of two skewHamiltonian matrices?' Linear and Multilinear Algebra, 63 (8). 1531  1552. ISSN 03081087

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Abstract
The mapping (Formula presented.) , where the matrices (Formula presented.) are skewHamiltonian 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 skewHamiltonian 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 skewHamiltonian matrices. Along the way, we discuss the connections of this problem with several existing results in matrix theory.
Item Type:  Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science and Health > Mathematical Sciences, Department of 
Depositing User:  Jim Jamieson 
Date Deposited:  20 Oct 2015 13:28 
Last Modified:  29 Mar 2021 12:15 
URI:  http://repository.essex.ac.uk/id/eprint/15326 
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