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Summation-By-Parts (SBP) methods provide a systematic way of constructingprovably stable numerical schemes. However, many proofs of convergence andaccuracy rely on the assumption that the SBP operator possesses a particulareigenvalue property. In this note, three results pertaining to this propertyare proven. Firstly, the eigenvalue property does not hold for all nullspaceconsistent SBP operators. Secondly, this issue can be addressed withoutaffecting the accuracy of the method by adding a specially designed,arbitrarily small perturbation term to the SBP operator. Thirdly, allpseudospectral methods satisfy the eigenvalue property.

On an eigenvalue property of Summation-By-Parts operators