The first order density matrix:
$\rho(r_{1}, r_{2}) = \sum_{i=1}^{N}\psi_{i}(r_{1})\psi_{i}^{*}(r_{2})$ where $\psi$'s are wavefunctions and the $r$'s are real coordinates.
If $r_{1}=r_{2}$ then the density matrix is the density.
How should I convince myself of this?