First thought: the curve in that first plot reflects the pseudospectrum? (https://en.wikipedia.org/wiki/Pseudospectrum https://en.wikipedia.org/wiki/Pseudospec

First thought: the curve in that first plot reflects the pseudospectrum? (https://en.wikipedia.org/wiki/Pseudospectrum https://en.wikipedia.org/wiki/Pseudospectrum) Spectra of nonnormal matrices can be very hard to calculate accurately.