  Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured
the wavefunction by weakly measuring a variable followed by a normal (i.e.
`strong') measurement of the complementary variable. We generalize this method
to mixed states by considering the weak measurement of the product of the two
observables, which, as a non-Hermitian operator, is normally unobservable. This
generalized method provides mixed states an operational definition related to
the operator representation proposed by Dirac. Uniquely, it can be performed
`in situ', determing the quantum state without destroying it.
