tr(σ_iσ_j) = 2δ_{ij}, [σ_x,σ_y] = 2iσ_z (exact)

Closed-form matrix-algebra verification of the Pauli algebra. Using sympy Matrix objects: (i) tr(σ_xσ_x) = tr(σ_yσ_y) = tr(σ_zσ_z) = 2 exactly, and tr(σ_xσ_y) = tr(σ_xσ_z) = tr(σ_yσ_z) = 0 exactly — the six traces collapsing to 2·δ_{ij}…