Several observations on symplectic, Hamiltonian, and skew-Hamiltonian matrices

被引：11

作者：

Fassbender, H

Ikramov, KD ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow 119899, Russia

[2] TU Braunschweig, Inst Computat Math, D-38023 Braunschweig, Germany

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 400卷

关键词：

symplectic matrix; Hamiltonian matrix; skew-Hamiltonian matrix; conjugate symplectic matrix; J-Hermitian matrix; J-skew-Hermitian matrix; singular value decomposition; definite hermitian pair;

D O I：

10.1016/j.laa.2004.12.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a Hamiltonian/skew-Hamiltonian version of the classical theorem relating strict equivalence and T-congruence between pencils of complex symmetric or skew-symmetric matrices. Then, we give a pure symplectic variant of the recent result of Xu concerning the singular value decomposition of a conjugate symplectic matrix. Finally, we discuss implications that can be derived from Veselic's result on definite pairs of Hermitian matrices for the skew-Hamiltonian situation. (c) 2005 Published by Elsevier Inc.

引用

页码：15 / 29

页数：15

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