(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 ifyexists in all R^{perpendicular}_{a1}then Ayexists in all R^{perpendicular}_{a1}

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 mappingyonto 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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# Operator acting in orthogonal subspace

Can you offer guidance or do you also need help?

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