  Geometrical structures of quantum mechanics provide us with new insightful
results about the nature of quantum theory. In this work we consider mixed
quantum states represented by finite rank density operators. We review our
geometrical framework that provide the space of density operators with
Riemannian and symplectic structures, and we derive a geometric uncertainty
relation for observables acting on mixed quantum states. We also give an
example that visualizes the geometric uncertainty relation for
spin-$\frac{1}{2}$ particles.
