  It is shown that the geometry of quantum theory can be derived from
geometrical structure that may be considered more fundamental. The basic
elements of this reconstruction of quantum theory are the natural metric on the
space of probabilities (information geometry), the description of dynamics
using a Hamiltonian formalism (symplectic geometry), and requirements of
consistency (K\"{a}hler geometry). The theory that results is standard quantum
mechanics, but in a geometrical formulation that includes also a particular
case of a family of nonlinear gauge transformations introduced by Doebner and
Goldin. The analysis is carried out for the case of discrete quantum mechanics.
The work presented here relies heavily on, and extends, previous work done in
collaboration with M. J. W. Hall.
