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 $A$.
Categories: math.FA