On the resolution of a double determinant

The resolution of a double determinant into a sum of spin-free orthogonal spin eigenfunctions is presented; its equivalent resolution of a spin function product θ^M₀ is also given. Furthermore, a more general resolution of a Slater determinant into all spin eigenfunctions with S ≥ M is also obtained. Present work has also provided a method to calculate the linear coefficients in the expression of the primitive θ^M_i in terms of the linear combination of spin eigenfunctions X? (S, M).