  The reaction anti-proton + proton -> anti-\Lambda + \Lambda -> anti-proton +
\pi^+ + proton + \pi^- has been measured with high statistics at anti-proton
beam momentum of 1.637 GeV/c. The use of a transversely-polarized frozen-spin
target combined with the self-analyzing property of \Lambda/anti-\Lambda decay
allows access to unprecedented information on the spin structure of the
interaction. The most general spin-scattering matrix can be written in terms of
eleven real parameters for each bin of scattering angle, each of these
parameters is determined with reasonable precision. From these results all
conceivable spin-correlations are determined with inherent self-consistency.
Good agreement is found with the few previously existing measurements of spin
observables in anti-proton + proton -> anti-\Lambda + \Lambda near this energy.
Existing theoretical models do not give good predictions for those
spin-observables that had not been previously measured.
