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Proof Hint/Help

  1. May 12, 2005 #1
    Hi everyone,

    Let T be a linear operator on nxn Matrices with real entries defined by
    T(A) = transpose(A).

    Show that +-1 are the only eigenvalues of T.

    Any tips on how to start this. I thought about writing the matrix representation relative to the standard basis, but it seemed really messy/tedious to write that out in general. Is there an easier way, or is that the only way to go?
  2. jcsd
  3. May 12, 2005 #2
    use the fact that T^2 = id
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