Hamiltonian square roots of skew-Hamiltonian matrices

Citation
H. Fassbender et al., Hamiltonian square roots of skew-Hamiltonian matrices, LIN ALG APP, 287(1-3), 1999, pp. 125-159
Citations number
24
Categorie Soggetti
Mathematics
Journal title
LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN journal
00243795 → ACNP
Volume
287
Issue
1-3
Year of publication
1999
Pages
125 - 159
Database
ISI
SICI code
0024-3795(19990115)287:1-3<125:HSROSM>2.0.ZU;2-J
Abstract
We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construct ion shows how one may bring any such W into a real quasi-Jordan canonical f orm via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all such square roots. Some extensions to complex matrices a re also presented. (C) 1999 Elsevier Science Inc. All rights reserved.