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Math Help - 6x6 Jordan Canonical Form

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    6x6 Jordan Canonical Form

    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?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: 6x6 Jordan Canonical Form

    Quote Originally Posted by dwsmith View Post
    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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