  The matrix affine Poisson space (M_{m,n}, pi_{m,n}) is the space of complex
rectangular matrices equipped with a canonical quadratic Poisson structure
which in the square case m=n reduces to the standard Poisson structure on
GL_n(C). We prove that the Hamiltonian flows of all minors are complete. As a
corollary we obtain that all Kogan-Zelevinsky integrable systems on M_{n,n} are
complete and thus induce (analytic) Hamiltonian actions of C^{n(n-1)/2} on
(M_{n,n}, pi_{n,n}) (as well as on GL_n(C) and on SL_n(C)).
  We define Gelfand-Zeitlin integrable systems on (M_{n,n}, pi_{n,n}) from
chains of Poisson projections and prove that their flows are also complete.
This is an analog for the quadratic Poisson structure pi_{n,n} of the recent
result of Kostant and Wallach [KW] that the flows of the complexified classical
Gelfand-Zeitlin integrable systems are complete.
