Spin-Density-Matrix Analysis. Positivity Conditions and Eberhard-Good Theorem

We derive the conditions that the positive-definiteness of the spin density matrix implies on its multipole parameters. We also derive the general conditions imposed by the Eberhard-Good theorem. General formulas are given for arbitrary spin $j$, and detailed results are worked out for $j=1\mathrm{}$ and $j=\frac{3}{2}$. Some applications of these results to spin determination are considered.