  It turns out that a parametrization of degenerate density matrices requires a
parametrization of $\mathfrak{F}=U(n)/({U(k_1)\times U(k_2)\times \cdots \times
U(k_m)})\quad n=k_1 +\cdots + k_m $ where $U(k)$ denotes the set of all unitary
$k\times k$-matrices with complex entries. Unfortunately the parametrization of
this quotient space is quite involved. Our solution does not rely on Lie
algebra methods {directly,} but succeeds through the construction of suitable
sections for natural projections, by using techniques from the theory of
homogeneous spaces. We mention the relation to the Lie algebra back ground and
conclude with two concrete examples.
