  We study the description of Schwarzschild black holes, of entropy S, within
matrix theory in the regime $N \ge S \gg 1$. We obtain the most general matrix
theory equation of state by requiring that black holes admit a description
within this theory. It has a recognisable form in various cases. In some cases
a D dimensional black hole can plausibly be thought of as a $\tilde{D} = D + 1$
dimensional black hole, described by another auxiliary matrix theory, but in
its $\tilde{N} \sim S$ regime. We find what appears to be a matrix theory
generalisation to higher dynamical branes of the normalisation of dynamical
string tension, seen in other contexts. We discuss a further possible
generalisation of the matrix theory equation of state. In a special case, it is
governed by $N^3$ dynamical degrees of freedom.
