  As far as entanglement is concerned, two density matrices of $n$ particles
are equivalent if they are on the same orbit of the group of local unitary
transformations, $U(d_1)\times...\times U(d_n)$ (where the Hilbert space of
particle $r$ has dimension $d_r$). We show that for $n$ greater than or equal
to two, the number of independent parameters needed to specify an $n$-particle
density matrix up to equivalence is $\Pi_r d_r^2 - \sum_r d_r^2 + n - 1$. For
$n$ spin-${1\over 2}$ particles we also show how to characterise generic
orbits, both by giving an explicit parametrisation of the orbits and by finding
a finite set of polynomial invariants which separate the orbits.
