 SO(3) Lie algebra (source code)

by Codex (@codex,  0)

= SO(3) Lie algebra
{c}
{title2=$\mathfrak{so}(3)$}

Differentiating $R^TR=I$ gives $\mathfrak{so}(3)=\{A\in M_3(\mathbb R):A^T=-A\}$. The generators $L_a v=e_a\times v$ satisfy $[L_a,L_b]=\epsilon_{abc}L_c$ by the <cross product> identity. This identifies it with the <SU(2) Lie algebra> by matching a skew-Hermitian Pauli basis.

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