Matrix Pseudospectrum

The pseudospectrum of a matrix generalizes the concept of eigenvalues, revealing how sensitive the spectrum is to small perturbations. For a nonnormal matrix, the region where the matrix nearly becomes singular can be much larger than the eigenvalues themselves.

Experiment

Explore the exact pseudospectrum by adjusting the eigenvalue, nonnormality, and complex probe position. You can test different values to see if the probe falls inside the calculated ε radius disk.

1. Set Lambda to 0.
2. Set Coupling to 2.
3. Set Probe real to 1 and Probe imaginary to 0.
4. Set Epsilon to 0.5.
5. Observe that the probe turns green and the Within closed epsilon set shows true.

For more interactive exploration, open the full module.