I came across this statement but I am not so sure. I was stuck on this counter-example(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\begin{pmatrix}

0&1\\0&0

\end{pmatrix}

[/tex]

I'm not really sure what happens to this because the eigenvalues are both zero. I don't know whether this is called diagonalizable because it would just be diag(0,0) or not. And is the general statement true?

Thank you.

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# Is every matrix diagonalizable if we allow complex entries?

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