Pauli Matrices

These are 3 matrixes used in Quantum Mechanics that are Hermitian Matrixes

Matrixes

$I={\sigma }_0$

$$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$

$X={\sigma }_1$

$$\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$$

$Y={\sigma }_2$

$$\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right]$$

$Z={\sigma }_3$

$$\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$$

Theorems

• Pauli Matrices form a Group
• Pauli Matrices are Unitary