  We propose a method for the spectral analysis of unbounded operator matrices
in a general setting which fully abstains from standard perturbative arguments.
Rather than requiring the matrix to act in a Hilbert space $\mathcal{H}$, we
extend its action to a suitable distributional triple $\mathcal{D} \subset
\mathcal{H} \subset \mathcal{D}_-$ and restrict it to its maximal domain in
$\mathcal{H}$. The crucial point in our approach is the choice of the spaces
$\mathcal{D}$ and $\mathcal{D}_-$ which are essentially determined by the Schur
complement of the matrix. We show spectral equivalence between the resulting
operator matrix in $\mathcal{H}$ and its Schur complement, which allows to pass
from a suitable representation of the Schur complement (e.g. by generalised
form methods) to a representation of the operator matrix. We thereby generalise
classical spectral equivalence results imposing standard dominance patterns.
  The abstract results are applied to damped wave equations with possibly
unbounded and/or singular damping, to Dirac operators with Coulomb-type
potentials, as well as to generic second order matrix differential operators.
By means of our methods, previous regularity assumptions can be weakened
substantially.
