# Defintion The Pauli matrices are given by: $ \begin{align} \sigma_1 = \sigma_\mathrm{x} &= \begin{pmatrix} 0&1\\ 1&0 \end{pmatrix} \\ \sigma_2 = \sigma_\mathrm{y} &= \begin{pmatrix} 0& -i \\ i&0 \end{pmatrix} \\ \sigma_3 = \sigma_\mathrm{z} &= \begin{pmatrix} 1&0\\ 0&-1 \end{pmatrix} \\ \end{align} $ They are [[Hermitian Operator|Hermitian]] and [[Unitary Operator|unitary]]. Alternative symbols include $\tau$ and $\rho$. Together with the identity matrix, they form a basis for the real vector space of $2 \times 2$ Hermitian matrices.