Author(s) :
Christian Mehl
,
André Ran
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2017
MSC 2000
- 15A33 Matrices over special rings
-
15A18 Eigenvalues, singular values, and eigenvectors
Abstract :
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 different: 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.
Keywords :
quaternions, eigenvalues, perturbation theory, low rank perturbations