Minimal Polynomial and Jordan Form
نویسنده
چکیده
Let V be a vector space over some field k, and let α : V V be a linear map (an ‘endomorphism of V ’). Given any polynomial p with coefficients in k, there is an endomorphism p(α) of V , and we say that p is an annihilating polynomial for α if p(α) = 0. Our first major goal is to see that for any α, the annihilating polynomials can easily be classified: they’re precisely the multiples of a certain polynomial mα. We reach this goal on the next page. Let us say that a polynomial m is a minimal polynomial for α (note: ‘a’, not ‘the’) if:
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