Parametrizations of the spin density matrix

We propose for the spin density matrix two parametrizations which automatically fulfil non-negativity conditions, without setting any bound on parameters. The first one relies a theorem, that we prove, and it is rather simple easily adaptable to some specific reactions, where, example, parity conserved or angular momentum conservation entails selection rules. Moreover, in case when rank less than order of matrix, show how improve fits data, either by implementing previous suggestions, elaborating an alternative method, prove second theorem. Our parametrization variant treatments, appears suitable particular processes. discuss about possibility inferring elements from differential decay width. Last, illustrate various examples current interest, both strong weak decays; them may be helpful investigation physics beyond standard model.