  We discuss the problem of adding random matrices, which enable us to study
Hamiltonians consisting of a deterministic term plus a random term. Using a
diagrammatic approach and introducing the concept of ``gluon connectedness," we
calculate the density of energy levels for a wide class of probability
distributions governing the random term, thus generalizing a result obtained
recently by Br\'ezin, Hikami, and Zee. The method used here may be applied to a
broad class of problems involving random matrices.
