We write down the spin density matrix of the reaction \overline {p} p\rightarrow \overline  \Lambda  \Lambda  in the usual matrix form, its elements are simply given as combinations of the spin observables, which have been measured at CERN with a polarized proton target. Then, we show that the standard properties of any density matrix applied to the matrix obtained allow to carry out a number of interesting, model independent and non-trivial inequalities on spin observables.

PACS numbers: 24.70.+s, 13.75.Cs, 13.75.Ev, 02.10.Yn