Figure 2.

Illustration of the structural stability ordering (3.9). We randomly generated 1000 stable 3×3 matrices. Entries were independently drawn from a normal distribution of zero mean and unit variance, discarding unstable matrices. We see that the stochastic structural stability of a matrix, ${\mathcal{S}}_{\mathrm{STR}}^{\mathrm{w}}$, can be much smaller than the smallest constant complex change needed to destabilize that matrix, ${\mathcal{S}}_{\mathrm{STR}}^c$. The equality ${\mathcal{S}}_{\mathrm{STR}}^{\mathrm{w}}=2{\mathcal{S}}_{\mathrm{STR}}^c$ is attained for normal matrices.