Paulimatrix

$\sigma _{x}={\begin{pmatrix}0&1\\1&0\end{pmatrix}}\,,\quad \sigma _{y}={\begin{pmatrix}0&-\mathrm {i} \\\mathrm {i} &0\end{pmatrix}}\,,\quad \sigma _{z}={\begin{pmatrix}1&0\\0&-1\end{pmatrix}}\,.$