6x6 Jordan Canonical Form

**dwsmith** · November 30th 2011, 02:41 PM

A 6x6 matrix A has eigenvalue lambda of multiplicity 6 and the eigenspace has dimension 3. What are the possible Jordan Canonical Forms?

$\begin{bmatrix} \begin{bmatrix}6&1&0\\0&6&1\\0&0&6\end{bmatrix} \\ & \begin{bmatrix} 6&1&1\\6&1&1\\6&1&1\end{bmatrix}\end{bmatrix}$

Is this correct since there are 3 linear independent eigenvectors?

**FernandoRevilla** · November 30th 2011, 08:56 PM

Originally Posted by dwsmith

Is this correct since there are 3 linear independent eigenvectors?

We have $\dim \ker(A-\lambda I)=3$ that is, the Jordan canonical form $J$ of $A$ has three blocks. So, there are three possible canonical forms according to the outline $6=1+1+4=1+2+3=2+2+2$ . Also, you wrote $6$ instead of $\lambda$ , and your second block is not a Jordan block.

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