Mirsky Singular-Value Stability

Compare singular-value movement with the total size of a matrix perturbation. Mirsky's theorem provides a bound stating that the absolute differences in singular values are bounded by the Frobenius norm of the perturbation matrix.

Experiment

Use the interactive module to visualize the effects of different perturbations on the singular values:

1. Set the Direction to "Shear".
2. Set the Perturbation magnitude to "1". Observe the Singular-value displacement (0.1882) is less than the Frobenius perturbation (1.0).
3. Change the Direction to "Diagonal" with magnitude "1". The Singular-value displacement grows to 1.414, which exactly matches the Frobenius bound. This shows the bound is tight for diagonal changes.