  We show that if in the particle beam there are linear correlations between
energy of particles and their transverse positions and momenta (linear beam
dispersions), then the transverse projected emittances always can be reduced by
letting the beam to pass through magnetostatic system with specially chosen
nonzero lattice dispersions. The maximum possible reduction of the transverse
projected emittances occurs when all beam dispersions are zeroed, and the
values of the lattice dispersions required for that are completely defined by
the values of the beam dispersions and the beam rms energy spread and are
independent from any other second-order central beam moments. Besides that, we
prove that, alternatively, one can also use the lattice dispersions to remove
linear correlations between longitudinal positions of particles and their
transverse coordinates (linear beam tilts), but in this situation solution for
the lattice dispersions is nonunique and the reduction of the transverse
projected emittances is not guaranteed.
