Expanding Hermitian operators in a basis of projectors on coherent spin states

The expectation values of a Hermitian operator (A) over cap in (2s + 1)(2) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2s + 1)(2) coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system. The result guarantees that (almost) any experimentally desirable choice of directions is appropriate for reconstructing the state of a quantum spin by means of a Stem-Gerlach apparatus.