Assume we have a certain particle—for example, a proton—in a quantum state | ψ ψ ⟩ ⟩ . If we apply one of the flavour rotations A to our particle, it enters a new quantum state which we can call A | ψ ψ ⟩ ⟩ . Depending on A, this new state might be a proton, or a neutron, or a superposition of a proton and a neutron, or various other possibilities. The set of all possible quantum states spans a vector space.