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Cayley - hamilton theorem

  1. Feb 14, 2006 #1
    i met a proof to cayley hamilton theorem and have some questions.

    It uses that lambda*I - A is invertible. But lambda is surely an eigenvalue of A and 1/(lamda*I - A) is not legit so how is it legal to use that.
     
  2. jcsd
  3. Feb 14, 2006 #2

    matt grime

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    Writing 1/(lambda*I-A) is also not allowed.

    Why is lambda an eigenvalue? Who says so? It is just a greek letter, probably representing some scalar. As it is unles you post all of the proof who can possibly say whether it is correct or not.
     
  4. Feb 14, 2006 #3
  5. Feb 14, 2006 #4
    Also I have some questions on these topics
     

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  6. Feb 14, 2006 #5
    The first sentence of the proof specifically states that "if lambda is not an eigenvalue of A"...
     
    Last edited: Feb 14, 2006
  7. Feb 17, 2006 #6

    0rthodontist

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    I don't know about cayley-hamilton but I do know that lambda is an eigenvalue of A iff lambda * I - A is NOT invertible.
     
  8. Feb 18, 2006 #7

    matt grime

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    Hmm? What do you mean by that (in regards to this post)?
     
  9. Feb 18, 2006 #8

    0rthodontist

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    Ah, I misinterpreted his post. At first reading I thought he was claiming that lambda * I - A is invertible meant that lambda was an eigenvalue of A. Now I see that he was claiming lambda was an eigenvalue of A separately from that statement.
     
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