Lipschitz properties of structure preserving matrix perturbations
Perturbation theory of general matrices with the same Jordan structure has been developed by I. Gohberg, P. Lancaster and the author in connection with properties of their invariant subspace lattices. In this paper the author continues the study of matrices with the same Jordan structure, in particular their perturbation analysis. The main results concern the Lipschitz property of canonical transformation matrices (CTM's). This property says that the CTM's can be chosen so that the change in these matrices is of the same magnitude as that of a matrix perturbation, provided the latter preserves the matrix structure under investigation. The author proves that, under small perturbations preserving the Jordan structure, CTM's have the Lipschitz property. Analogous results are obtained for matrices with additional structure, such as Hamiltonian, skew-Hamiltonian and symplectic, including the real and complex cases.
scientific article; zbMATH DE number 6072611
scientific article