Sensitivity of the eigenvalues of a defective matrix (Q789868)

\textit{G. H. Golub} and \textit{J. H. Wilkinson} [SIAM Rev. 18, 578-619 (1976; Zbl 0341.65027)] indicated that it is possible for a matrix to be highly defective without its eigenvalues being unduly sensitivity. However, it hasn't been interpreted yet. This paper gives an estimate of sensitivity of the eigenvalues for a defective matrix (so that for a general matrix). It generalizes not only all special results of Wilkinson, Stewart, Bauer and Fike, when the eigenvalue is simple and when the matrix is nondefective, but also it interprets this phenomenon.