Rank one perturbations of H -positive real matrices

Jordan Forms of Real and Complex Matrices under Rank One Perturbations

New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the complex case are proved as well for the real case and the assumptions on the genericity are weakened. Rank one perturbations that lead to maximal algebraic multiplicities of the “new” eigenvalues are ...

On Rank One H−3-Perturbations of Positive Self–adjoint Operators

Rank one H−3 perturbations of positive self–adjoint operators are constructed using a certain extended Hilbert space and regularization procedures. Applications to Schrödinger operators with point interactions are discussed.

On low rank perturbations of matrices

The article is devoted to different aspects of the question: ”What can be done with a matrix by a low rank perturbation?” It is proved that one can change a geometrically simple spectrum drastically by a rank 1 perturbation, but the situation is quite different if one restricts oneself to normal matrices. Also the Jordan normal form of a perturbed matrix is discussed. It is proved that with res...

Rank one perturbations of self-adjoint operators

Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations

We study the perturbation theory of structured matrices under structured rank one perturbations, and then focus on several classes of complex matrices. Generic Jordan structures of perturbed matrices are identified. It is shown that the perturbation behavior of the Jordan structures in the case of singular J-Hamiltonian matrices is substantially different from the corresponding theory for unstr...