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All normal matrices are non-defective, but are all non-defective matrices normal? I haven't been able to find anything about this online, so presumably it is not true. If this is so, could someone provide an example of a non-defective, non-normal matrix? Otherwise, a pointer towards a proof would be much appreciated!

A.Γ.
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Meep
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    Try $$ M=\begin{bmatrix}1 & 1\0 & 2\end{bmatrix}. $$ – A.Γ. Jan 01 '18 at 15:45
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    Isn't that the same question? https://math.stackexchange.com/questions/271869/diagonalizable-vs-normal – A.Γ. Jan 01 '18 at 15:51
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    @A.Γ.Indeed it is. Apologies. I was thinking about linear independence of eigenvectors and missing the absolutely obvious point that this is equivalent to diagonalisability. – Meep Jan 01 '18 at 16:54
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    @A.Γ.Would it be appropriate to close or delete the question? – Meep Jan 01 '18 at 16:54

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