  The MIMOME channel is a Gaussian wiretap channel in which the sender,
receiver, and eavesdropper all have multiple antennas. We characterize the
secrecy capacity as the saddle-value of a minimax problem. Among other
implications, our result establishes that a Gaussian distribution maximizes the
secrecy capacity characterization of Csisz{\'a}r and K{\"o}rner when applied to
the MIMOME channel. We also determine a necessary and sufficient condition for
the secrecy capacity to be zero. Large antenna array analysis of this condition
reveals several useful insights into the conditions under which secure
communication is possible.
