  We describe explicitly the admissible families of minors for the totally
nonnegative cells of real matrices, that is, the families of minors that
produce nonempty cells in the cell decompositions of spaces of totally
nonnegative matrices introduced by A. Postnikov. In order to do this, we relate
the totally nonnegative cells to torus orbits of symplectic leaves of the
Poisson varieties of complex matrices. In particular, we describe the minors
that vanish on a torus orbit of symplectic leaves, we prove that such families
of minors are exactly the admissible families, and we show that the nonempty
totally nonnegative cells are the intersections of the torus orbits of
symplectic leaves with the spaces of totally nonnegative matrices.
