  Summation-By-Parts (SBP) methods provide a systematic way of constructing
provably stable numerical schemes. However, many proofs of convergence and
accuracy rely on the assumption that the SBP operator possesses a particular
eigenvalue property. In this note, three results pertaining to this property
are proven. Firstly, the eigenvalue property does not hold for all nullspace
consistent SBP operators. Secondly, this issue can be addressed without
affecting the accuracy of the method by adding a specially designed,
arbitrarily small perturbation term to the SBP operator. Thirdly, all
pseudospectral methods satisfy the eigenvalue property.
