Weyl Eigenvalue Perturbation Bound

Compare eigenvalue movement with a guaranteed perturbation interval.

Experiment

Open the Weyl Eigenvalue Perturbation Bound module to see how the eigenvalues shift under different perturbations.

1. Set the Base matrix to Repeated to see that Weyl's bound holds even when the original matrix has repeated eigenvalues (2I).
2. Change the Perturbation to Identity. Notice that adding tI shifts both eigenvalues exactly by t, making the maximum shift exactly equal to the spectral norm (bound slack is zero).
3. Adjust the Perturbation size using the slider to see the guaranteed bound interval (shaded region) grow and shrink, while the perturbed eigenvalues always remain within the interval.