In another question, a user kindly explained that not all Involutory matrices are Normal. I thought they were 'very Normal': both Unitary and Hermitian, but clearly they are neither always Unitary nor Hermitian.
Could you please give an example of an Involutory matrix which is not Normal?
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$\begingroup$I just worked it out. Hope it helps somebody!
\begin{pmatrix} 0 & 2 \\ 0.5 & 0 \end{pmatrix}
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