The Pauli spin matrices represent the three (x,y,z) spin operators acting on a spin 1/2 particle (such as an electron): that is to say that the spin operator can be written as **S** = (1/2)(h-bar)**σ**. They are conventionally written as:

σ_{1} = (0 1)
(1 0)
σ_{2} = (0 -i)
(i 0)
σ_{3} = (1 0)
(0 -1)

They are each

unitary,

hermitian and

trace-free (indeed, the form a basis of sl

_{2}(

**C**)). Also, they

anticommute in pairs, and satisfy the

commutation relation [ σ

_{i},σ

_{j} ] = 2iε

_{ijk}σ

_{k}.