Cayley-Hamilton Theorem
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Let \(F\) be a field, and let \(V\) be a finite dimensional \(F\)-vector space. If \(t : V → V\) is a linear transformation, then \(m_t\mid c_t \), and hence \(c_t(t) = 0\). Similarly, for any matrix \(A ∈ M_n(F)\) over a field \(F\) we have \(m_A|c_A\) and \(c_A(A) = 0\).
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