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    I have attached a proof below and just wondering whether someone could explain to me the last part. I don't understand why  m_A is a zero of  \chi_{m_a(A)}=\chi_Z = X^n ?  m_A is the minimum polynomial and Z is the zero matrix.
    EDIT:  \chi_A is the characteristic polynomial.
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    It's not m_A that is a zero, but m_A (\lambda), and that's zero because you can just substitute it in!
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    (Original post by Zhen Lin)
    It's not m_A that is a zero, but m_A (\lambda), and that's zero because you can just substitute it in!
    Thanks for the reply, but where does x^n come from? I don't know how that got there.
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    (Original post by JBKProductions)
    Thanks for the reply, but where does x^n come from? I don't know how that got there.
    Because, m_A(A) = 0, and the characteristic polynomial of a n \times n zero matrix is x^n.
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    Thanks.

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