Pauli algebra: tr(σ_iσ_j) = 2δ_{ij}, [σ_i,σ_j] = 2iε_{ijk}σ_k

Pauli matrices σ_x, σ_y, σ_z span the three-dimensional real vector space of 2×2 traceless Hermitian matrices and generate the Lie algebra su(2). Concretely σ_x = [[0,1],[1,0]], σ_y = [[0,−i],[i,0]], σ_z = [[1,0],[0,−1]]. Algebraic…