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Transpose Eigenvector Proof

  1. Apr 7, 2009 #1
    Eigenvalue and eigenvector for a symmetric matrix

    1. The problem statement, all variables and given/known data

    Let A be a n by n real matrix with the property that the transpose of A equals A. Show that if Ax = lambda x, for some non-zero vector x in C(n) then lambda is real, and the real part of x is an eigenvector of A.


    2. Relevant equations



    3. The attempt at a solution

    Since transpose of A equals A, A must be a symmetric matrix. But beyond that, I don't know where to start. Any help would be appreciated!
     
    Last edited: Apr 7, 2009
  2. jcsd
  3. Apr 7, 2009 #2
    Can anyone offer any insight?
     
  4. Apr 8, 2009 #3

    Cyosis

    User Avatar
    Homework Helper

    Start out with [itex](\boldsymbol{v},A \boldsymbol{v})[/itex]. In case this notation is unknown to you it's supposed to represent the complex inner product.
     
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