  We consider random non-normal matrices constructed by removing one row and
column from samples from Dyson's circular ensembles or samples from the
classical compact groups. We develop sparse matrix models whose spectral
measures match these ensembles. This allows us to compute the joint law of the
eigenvalues, which have a natural interpretation as resonances for open quantum
systems or as electrostatic charges located in a dielectric medium.
  Our methods allow us to consider all values of $\beta>0$, not merely
$\beta=1,2,4$.
