LOW RANK PERTURBATIONS OF QUATERNION MATRICES

Low rank perturbations of right eigenvalues of quaternion matrices are considered. For real and complex matrices
it is well known that under a generic rank-k perturbation the k largest Jordan blocks of a given eigenvalue will disappear while
additional smaller Jordan blocks will remain. In this paper, it is shown that the same is true for real eigenvalues of quaternion
matrices, but for complex nonreal eigenvalues the situation is dierent: not only the largest k, but the largest 2k Jordan
blocks of a given eigenvalue will disappear under generic quaternion perturbations of rank k. Special emphasis is also given to
Hermitian and skew-Hermitian quaternion matrices and generic low rank perturbations that are structure-preserving.