Pauli Matrices

SU(2)

The matrix group SU(2) is a Lie group, and its Lie algebra is the set of the anti-Hermitian 2×2 matrices with trace 0. Direct calculation shows that the Lie algebra su(2) is the 3-dimensional real algebra spanned by the set {}. In symbols,

As a result, s can be seen as infinitesimal generators of SU(2).