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Let $\ m_T(x)=\prod p_i(x)^{m_i}$ be the minimal polynomial of an operator $T$ and $\ p_T(x)=\prod p_i(x)^{h_i}$ the characteristic polynomial.

Let $ V_i= \operatorname{Ker}{(p_i(x))^{h_i}} $

I don't understand why $\dim V_i = \deg\,(p_i)*h_i$

Thanks.

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    Are we assuming $p_i$ are irreducible over our ground field?2011-06-28
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    @Arturo in the name of the question he sais "irred factors". So I guess the answer to your question is yes.2011-06-28
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    @Listing: Yes, but posts should be self-contained. I'm not usually required to look in the spine of the book (or the title page of a book) for the hypothesis of a theorem stated in the book; are you?2011-06-28
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    If you see it that way, you are right :)2011-06-29

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