The Cayley Hamilton theorem states for a transformation $T:V \rightarrow V$ then the characteristic equation of $T$, $X_T(x)$ has the property that $X_T(A)=0$ where A is the matrix representation of the transformation. Equivalently $X_A(A)=0$?
Can anyone explain to me why this is equivalent to $m_T|X_T$ where $m_T$ is the minimum polynomial of $T$?
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sign. $\endgroup$ – Pierre-Yves Gaillard Jan 4 '12 at 19:30