# Jordan Canonical form 4x4 matrix

Compute the Jordan Canonical form of $\begin{bmatrix}0 & 1 & 0 & 0\\0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0\end{bmatrix}$

I don't know what to do after computing the characteristic polynomial, which i got $x^4$=0. This would give us an eigenvalue of x=0 of multiplicity 4.

Any thoughts/comments on where to go after this? Thanks so much!

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Huh? Isn't the matrix already a Jordan form? – user1551 Nov 13 '13 at 9:07

Next you need to find the minimal polynomial. It is one of $x^2,x^3,x^4$. Use direct verification- here clearly matrix multiplied by itself gives zero, hence the minimal polynomial is $x^2$.Therefore largest Jordan block $J(0,l)$ is of size 2 (that occurs in JNF ) and 4 is the sum of the sizes of these Jordan blocks.