The group SU(3) is a subgroup of group U(3), the group of all 3×3 unitary matrices. The unitarity condition imposes nine constraint relations on the total 18 degrees of freedom of a 3×3 complex matrix. Thus, the dimension of the U(3) group is 9. Furthermore, multiplying a U by a phase, e leaves the norm invariant. Thus U(3) can be decomposed into a direct product U(1)×SU(3)/Z 3. Because of this additional constraint, SU(3) has dimension 8.