# Cayley - hamilton theorem

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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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.

http://www.math.chalmers.se/~wennberg/Undervisning/ODE/linalg.pdf [Broken]

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Also I have some questions on these topics

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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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0rthodontist
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.

matt grime