Hi everyone. I am studying 'identical particles' in quantum mechanics, and I have a problem with the properties of the Symmetrizer (S) and Antisymmetrizer (A) operators. S and A are hermitian operators. Therefore, for what I know, their set of eigenkets must constitute a basis of the space ket. However, the set of eigenkets of S (A) contains only symmetric (antisymmetric) kets. Given an arbitrary ket (not necessarily symmetrical or antisymmetrical), I don't think it is always possible to write it as linear combination of only symmetrical (antisymmetrical) kets. Therefore, I can't understand how the eigenkets of S (A) can constitute a basis of the space ket.