Positivity conditions on the spin density matrix: A simple parametrization

A simple parametrization of the spin density matrix $\rho$ is given which ensures that $\rho$ is a positive, Hermitian matrix which satisfies the parity symmetry conditions. There is a minimal number of parameters and they can vary independently; no complicated constraints on their allowed region of variation are required. A similar parametrization is given for the real part of $\rho$. Rank conditions, polarized targets, and angular distributions are also discussed.