# Homework Help: Operator acting in orthogonal subspace

1. Feb 7, 2009

### seek

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.

Last edited: Feb 7, 2009