User talk:Choco.litt

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And don't forget, the edit summary is your friend. :) – Oleg Alexandrov (talk) 04:47, 22 February 2007 (UTC)[reply]

Cayley Hamilton proof[edit]

Welcome to wikipedia from me too. I hope you have fun editing some articles here.

Please don't take it personally if I revert your edits to the Cayley-Hamilton theorem proof. The evaluation map used there is a homomorphism of k[t] modules, from V[t] to V, so there are no other matrices involved apart from A. Hence it does not make sense to say it is only a homomorphism over the center (centralizer) of A. If the proof used rings such as End(V)[t], then your correction/observation would be needed, but it doesn't.

Anyway, this proof needs to be made more accessible, so I intend to put some work in on it soon. Geometry guy 10:19, 22 February 2007 (UTC)[reply]

Oops[edit]

True, thanks for reverting it.

Daniel

(It is easier to keep a thread on the page on which it started.)

I've done some tidying up of the Cayley-Hamilton theorem proof now. I welcome your comments. Also, I realised that there is a point to what you said: namely, one needs to know that the composition of evaluation at A with matrix multiplication by t I - A is zero. Although this is obvious, it does secretly use the fact that t I - A is in the centralizer of A in polynomial matrices, just as you suggested. Anyway, feel free to make this point explicit in the article if you want to. Geometry guy 17:12, 22 February 2007 (UTC)[reply]