  For a general class of large non-Hermitian random block matrices $\mathbf{X}$
we prove that there are no eigenvalues away from a deterministic set with very
high probability. This set is obtained from the Dyson equation of the
Hermitization of $\mathbf{X}$ as the self-consistent approximation of the
pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation
from [arXiv:1604.08188v4] offers a unified treatment of many structured matrix
ensembles.
