If a given observable A is non-degenerate, there exists a unique basis formed by its eigenvectors. On the other hand, if one or several eigenvalues of A ^ ^ are degenerate, specifying an eigenvalue is not sufficient to characterize a basis vector. If, by choosing an observable B ^ ^ , which commutes with A ^ ^ , it is possible to construct an orthonormal basis of eigenvectors common to A ^ ^ and B ^ ^ , which is unique, for each of the possible pairs of eigenvalues {a,b}, then A ^ ^ and B ^ ^ are said to form a complete set of commuting observables. However, if a unique set of eigenvectors can still not be specified, for at least one of the pairs of eigenvalues, a third observable C ^ ^ , which commutes with both A ^ ^ and B ^ ^ can be found such that the three form a complete set of commuting observables.