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Operator acting in orthogonal subspace

  1. Feb 7, 2009 #1
    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?

    Wikipedia tells me that a normal operator is indeed a linear operator. I think I can do this now.
    Last edited: Feb 7, 2009
  2. jcsd
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