ε-pseudospectrum: where eigenvalues can go under ε-perturbation (Trefethen 1997)
The ε-pseudospectrum of A is:
For non-normal matrices, eigenvalues are highly sensitive: a tiny perturbation can move them far. The pseudospectrum reveals the true "operational" spectrum.
Grcar and Jordan matrices are prototypically non-normal — their pseudospectra are enormous compared to their actual eigenvalues.