# Rational canonical form of $\begin{bmatrix} 4 & 0 & 0 \\ 4 & 12 & 4 \\ -8 & -16 & -4 \\ \end{bmatrix}$

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 $$\begin{bmatrix} 4 & 0 & 0 \\ 0 & 0 & -16 \\ 0 & 1 & 8 \\ \end{bmatrix}$$?

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