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Proof help.

I have attached a proof below and just wondering whether someone could explain to me the last part. I don't understand why mA m_A is a zero of χma(A)=χZ=Xn \chi_{m_a(A)}=\chi_Z = X^n ? mA m_A is the minimum polynomial and Z is the zero matrix.
EDIT: χA \chi_A is the characteristic polynomial.
(edited 11 years ago)
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Reply 2
It's not mAm_A that is a zero, but mA(λ)m_A (\lambda), and that's zero because you can just substitute it in!
Original post by Zhen Lin
It's not mAm_A that is a zero, but mA(λ)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.
Reply 4
Original post by JBKProductions
Thanks for the reply, but where does x^n come from? I don't know how that got there.


Because, mA(A)=0m_A(A) = 0, and the characteristic polynomial of a n×nn \times n zero matrix is xnx^n.
Thanks.

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