This greater mathematical precision for example makes it possible to assess how singlets and doublets behave under rotation operations. Since a spin  electron transforms as a doublet under rotation, its experimental response to rotation can be predicted by using the fundamental representation of that doublet, specifically the Lie group SU(2). Applying the operator formula_9 to the spin state of the electron thus will always result in formula_10, or spin , since the spin-up and spin-down states are both eigenstates of the operator with the same eigenvalue.