Cayley - hamilton theorem

  • Thread starter vabamyyr
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  • #1
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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.
 

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  • #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.
 
  • #3
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http://www.math.chalmers.se/~wennberg/Undervisning/ODE/linalg.pdf [Broken]
 
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  • #5
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The first sentence of the proof specifically states that "if lambda is not an eigenvalue of A"...
 
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  • #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.
 
  • #7
matt grime
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Hmm? What do you mean by that (in regards to this post)?
 
  • #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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