# Question: one of the best known results of eigenvalue perturbation theory...

###### Question details

One of the best known results of eigenvalue perturbation theory is the Bauer-Fike theorem. Suppose A E C^mxm is diagonalizable with A = V AV^-1, and let

be arbitrary. Then every eigenvalue of lies in at least one of the m circular disks in the complex plane of radius centered at the eigenvalues of A, where is the 2-norm condition number

Suppose A is normal. Show that for each eigenvalue of , there is an eigenvalue , of A such that