1. The problem statement, all variables and given/known data Consider a normal operator A If Rperpendiculara1 is the orthogonal complement to the subspace of eigenvectors of A with eigenvalue a1, show that if y exists in all Rperpendiculara1 then Ay exists in all Rperpendiculara1 3. The attempt at a solution This could be answered very simply, if I knew that all normal operators were linear. Were that the case, A would simply be mapping y onto the subspace in which it already existed. Am I right? *Edit: Wikipedia tells me that a normal operator is indeed a linear operator. I think I can do this now.