  Recent work has revealed that the wave function of a pure state can be
measured directly and that complementary knowledge of a quantum system can be
obtained simultaneously by weak measurements. However, the original scheme
applies only to pure states, and it is not efficient because most of the data
are discarded by post-selection. Here, we propose tomography schemes for pure
states and for mixed states via weak measurements, and our schemes are more
efficient because we do not discard any data. Furthermore, we demonstrate that
any matrix element of a general state can be directly read from an appropriate
weak measurement. The density matrix (with all of its elements) represents all
that is directly accessible from a general measurement.
