  This paper focuses on the geometric phase of general mixed states under
unitary evolution. Here we analyze both non-degenerate as well as degenerate
states. Starting with the non-degenerate case, we show that the usual procedure
of subtracting the dynamical phase from the total phase to yield the geometric
phase for pure states, does not hold for mixed states. To this end, we furnish
an expression for the geometric phase that is gauge invariant. The parallelity
conditions are shown to be easily derivable from this expression. We also
extend our formalism to states that exhibit degeneracies. Here with the
holonomy taking on a non-abelian character, we provide an expression for the
geometric phase that is manifestly gauge invariant. As in the case of the
non-degenerate case, the form also displays the parallelity conditions clearly.
Finally, we furnish explicit examples of the geometric phases for both the
non-degenerate as well as degenerate mixed states.
