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Eigenvalue question

  1. Nov 1, 2004 #1
    if an operator O has the property that O^{4}f(x)=f(x), what are the eigenvalues of O? any hints on how to go about this?
  2. jcsd
  3. Nov 1, 2004 #2


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    Since [itex]O^4[/itex] is the identity, it has all eigenvalues one.
    If [itex]O[/itex] has an eigenvector f with eigenvalue [itex]\lambda[/itex], what can you tell about [itex]O^2[/itex]
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