For two commuting observables A and B, one can construct an orthonormal basis of the state space with eigenvectors common to the two operators. However, λ λ is a degenerate eigenvalue of A ^ ^ , then it is an eigensubspace of A ^ ^ that is invariant under the action of B ^ ^ , so the representation of B ^ ^ in the eigenbasis of A ^ ^ is not a diagonal but a block diagonal matrix, i.e. the degenerate eigenvectors of A ^ ^ are not, in general, eigenvectors of B ^ ^ . However, it is always possible to choose, in every degenerate eigensubspace of A ^ ^ , a basis of eigenvectors common to A ^ ^ and B ^ ^ .