1.4.2011

Jan Brandts (University of Amsterdam, The Netherlands)

Normality preserving perturbations and their effect on the eigenvalues

Summary:
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We revisit the normality preserving augmentation of normal matrices studied
by Ikramov and Elsner in 1998 and complement their results by showing how
the eigenvalues of the original matrix are perturbed by the augmentation.

Next, we study normality preserving normal perturbations of normal matrices.
All 2x2 and all rank-1 normality preserving normal perturbations are characterized.
For higher rank we restrict ourselves to essentially Hermitian perturbations.
Essentially Hermitian matrices often appear in both numerical and core
linear algebra. For each rank, the effect of the perturbation on the eigenvalues
of the original matrix is given. Simple examples complement the theory.