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Can anyone give me an example of a normal matrix that isn't unitary? Here, $A \in \mathbb{C^{n \times n}}$.

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Take every $A$ with $A=A^{H}$ where $H$ denotes the Hermitian transform(conjugate transposed). For example $A=\begin{pmatrix} 4 & 2i\\-2i & 4 \end{pmatrix}$

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