  In a previous paper (math-ph/0205016) an Euler angle parameterization for
SU(N) was given. Here we present a generalized Euler angle parameterization for
U(N). The formula for the calculation of the volume for U(N), CP(N) as well as
other SU(N) and U(N) cosets will also be given. In addition, the mixed and pure
state product measures for N-dimensional density matrices under this
parameterization will also be derived.
