Let A be an n x n matrix; denote its distinct eigenvalues by a_1,...,a_k and denote the index of a_i by d_i. How do I prove that the minimal polynomial is then:(adsbygoogle = window.adsbygoogle || []).push({});

m_A(s) = (s-a_1)^d_1*...*(s-a_k)^d_k

?

The characterstic polynomial is defined as:

p_A(s) = (s-a_1)*...*(s-a_n);

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# Homework Help: Minimal Polynomial A nxn Matrix

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