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What is the rational canonical form of $$ \begin{bmatrix} 4 & 0 & 0 \\ 4 & 12 & 4 \\ -8 & -16 & -4 \\ \end{bmatrix}$$

Its characteristic polynomial is $(x-4)^3$ and its minimal poly is $(x-4)^2$.

Does this mean its rational canonical form is $$ \begin{bmatrix} 4 & 0 & 0 \\ 0 & 0 & -16 \\ 0 & 1 & 8 \\ \end{bmatrix} $$?

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  • $\begingroup$ That is the correct rcf. Are you just looking for this confirmation? $\endgroup$ – Omnomnomnom Feb 16 at 13:05
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    $\begingroup$ Thnk you. Yes i am. $\endgroup$ – user593805 Feb 16 at 13:12

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