  Solving the exact renormalisation group equation a la Wilson-Polchinski
perturbatively, we derive a power-counting theorem for general matrix models
with arbitrarily non-local propagators. The power-counting degree is determined
by two scaling dimensions of the cut-off propagator and various topological
data of ribbon graphs. As a necessary condition for the renormalisability of a
model, the two scaling dimensions have to be large enough relative to the
dimension of the underlying space. In order to have a renormalisable model one
needs additional locality properties--typically arising from orthogonal
polynomials--which relate the relevant and marginal interaction coefficients to
a finite number of base couplings. The main application of our power-counting
theorem is the renormalisation of field theories on noncommutative R^D in
matrix formulation.
