Conservative perturbations of positive definite Hamiltonian matrices
Pierluigi Amodio, Felice Iavernaro, Donato Trigiante · Numerical Linear Algebra with Applications · 2004
Abstract We consider Hamiltonian matrices obtained by means of symmetric and positive definite matrices and analyse some perturbations that maintain the eigenvalues on the imaginary axis of the complex plane. To obtain this result we prove for such matrices the existence of a diagonal form or, alternatively by means of symplectic transformations, the existence of the simplest canonical form. Applications related to a pair of problems in the context of linear algebra and differential equations are also reported. Copyright © 2004 John Wiley & Sons, Ltd.