  In this paper we introduce a geometric framework for mixed quantum states
based on a K\"ahler structure. The geometric framework includes a symplectic
form, an almost complex structure, and a Riemannian metric that characterize
the space of mixed quantum states. We argue that the almost complex structure
is integrable. We also in detail discuss a visualizing application of this
geometric framework by deriving a geometric uncertainty relation for mixed
quantum states. The framework is computationally effective and it provides us
with a better understanding of general quantum mechanical systems.
