Matrix-valued shell of an operator or relation

The point spectrum and numerical range of a Hilbert-space operator are subsets of the complex plane. When in place of the operator one puts an arbitrary linear relation, they are naturally replaced by subsets of, respectively, the Riemann sphere and the ball bounded by the Riemann sphere. In this paper, the matrix-valued analogues are studied. The first two sections trace the analogy; in the final two sections it is shown how new phenomena appearing in the matrix version reflect specific singularities of the linear relation.