Suppose I want to write a general $2\times2$ special unitary matrix in a given basis, I can write it as such:$$\begin{pmatrix} \alpha & -\overline\beta\\ \beta & \overline \alpha\end{pmatrix}$$with $|\alpha|^2+|\beta|^2=1$. However I do not know if such a form exists for Clifford matrices/gates. Is there such a way to represent $2\times2$ or $4\times 4$ or even higher dimensions Clifford in terms of conditions between its matrix elements?
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