  If a nonnegative selfadjoint linear relation $A$ in a Hilbert space and a
closed subspace $\mathcal{S}$ are assumed to satisfy that the domain of $A$ is
invariant under the orthogonal projector onto $\mathcal{S},$ then $A$ admits a
particular matrix representation with respect to the decomposition $\mathcal{S}
\oplus \mathcal{S}^{\perp}$. This matrix representation of $A$ is used to give
explicit formulae for the Schur complement of $A$ on $\mathcal{S}$ as well as
the $\mathcal{S}-$compression of $A$.
