If two operators A ^ ^ and B ^ ^ commute, i.e., [ A ^ ^ , B ^ ^ ] = 0 , then for every eigenvector | ψ ψ ⟩ ⟩ of A ^ ^ , B ^ ^ | ψ ψ ⟩ ⟩ is also an eigenvector of A ^ ^ with the same eigenvalue. However, if this eigenvalue, say λ λ , is degenerate, it can be said that B ^ ^ | ψ ψ ⟩ ⟩ belongs to the eigenspace E λ λ of A ^ ^ , which is said to be globally invariant under the action of B ^ ^ .