The structure of alternating-Hamiltonian matrices

Generalizing results proved recently for the real and complex case, we show over all fields that every alternating-Hamiltonian matrix is similar to a block-diagonal matrix of the form A 0 0 A t , and that any two similar ones are similar by a symplectic transformation. Furthermore, every one is a sq...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2005-02, Vol.396, p.385-390
Main Author: Waterhouse, William C.
Format: Article
Language:English
Subjects:
Algebra
Alternating-Hamiltonian
Exact sciences and technology
Field theory and polynomials
Hamiltonian matrices
Linear and multilinear algebra, matrix theory
Mathematics
Pairs of alternating forms
Sciences and techniques of general use
Skew-Hamiltonian
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Generalizing results proved recently for the real and complex case, we show over all fields that every alternating-Hamiltonian matrix is similar to a block-diagonal matrix of the form A 0 0 A t , and that any two similar ones are similar by a symplectic transformation. Furthermore, every one is a square of a Hamiltonian matrix. The proofs use a structural idea drawn from the study of pairs of alternating forms. Counterexamples show that the definitions must be carefully chosen to work in characteristic 2.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2004.10.003