  This paper considers the problem of the multiple-input multiple-output (MIMO)
Gaussian broadcast channel with two receivers (receivers 1 and 2) and two
messages: a common message intended for both receivers and a confidential
message intended only for receiver 1 but needing to be kept asymptotically
perfectly secure from receiver 2. A matrix characterization of the secrecy
capacity region is established via a channel enhancement argument. The enhanced
channel is constructed by first splitting receiver 1 into two virtual receivers
and then enhancing only the virtual receiver that decodes the confidential
message. The secrecy capacity region of the enhanced channel is characterized
using an extremal entropy inequality previously established for characterizing
the capacity region of a degraded compound MIMO Gaussian broadcast channel.
