Note on structured indefinite perturbations to Hermitian matrices
Results of \textit{M. L. Overton} and \textit{P. van Dooren} [On computing the complex passivity radius. Proc. IEEE Conference on decision Control (to appear)] about certain structured perturbations of Hermitian matrices are generalised to the case of skew-Hermitian, Hamiltonian and skew-Hamiltonian matrices. The questions considered are the following: Is there a structured perturbation such that the perturbed matrix is singular? What is the smallest (in operator norm) such perturbation? These questions are answered for the abovementioned classes and for two classes of perturbations, additive ones and multiplicative ones. In the skew-Hamiltonian case also the distance to a matrix with a real eigenvalue is given. A numerical method to calculate these distances is sketched and an example is given.
scientific article; zbMATH DE number 5142295