Since the Pauli matrices do not commute, measurements of spin along the different axes are incompatible. This means that if, for example, we know the spin along the x axis, and we then measure the spin along the y axis, we have invalidated our previous knowledge of the x axis spin. This can be seen from the property of the eigenvectors (i.e. eigenstates) of the Pauli matrices that | ⟨ ⟨ ψ ψ x ± ± | ψ ψ y ± ± ⟩ ⟩ | 2 = | ⟨ ⟨ ψ ψ x ± ± | ψ ψ z ± ± ⟩ ⟩ | 2 = | ⟨ ⟨ ψ ψ y ± ± | ψ ψ z ± ± ⟩ ⟩ | 2 = 1 2 .