Bauer–Fike Nonnormal Bound

The Bauer-Fike theorem provides bounds on the eigenvalues of perturbed matrices. In the case of nonnormal matrices, the sensitivity of eigenvalues to perturbations is amplified by the condition number of the eigenvector matrix.

Experiment

Adjust the parameters to see the effects of nonnormality in the module:

1. Change the Eigenbasis shear to increase the nonnormality of the matrix.
2. Modify the Perturbation delta to alter the perturbation matrix E.
3. Observe how the condition number of V inflates the Bauer-Fike radius.
4. Notice when the eigenvalues become complex or defective (non-diagonalizable).