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## Homework Statement

Consider a normal operator A

If R

^{perpendicular}

_{a1}is the orthogonal complement to the subspace of eigenvectors of A with eigenvalue a1, show that if

**y**exists in all R

^{perpendicular}

_{a1}then A

**y**exists in all R

^{perpendicular}

_{a1}

## 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.

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