Perturbations of Eigenvalues of Non-normal Matrices
The problem considered is to give bounds for finite
perturbations of simple and multiple eigenvalues 
of nonnormal matrices, where these bounds are in terms
of the eigenvalues, the departure from normality, 
and the Frobenius norm of the perturbation matrix, but
not in terms of the eigen system.  The bounds which 
are derived are shown to be almost attainable for any set of matrices. 
CACM January, 1975
van der Sluis, A.
