回転行列
R ( α , β , γ , δ ) = [ 1 2 ( α 2 − γ 2 + δ 2 − β 2 ) i 2 ( γ 2 − α 2 + δ 2 − β 2 ) γ δ − α β i 2 ( α 2 + γ 2 − β 2 − δ 2 ) 1 2 ( α 2 + γ 2 + β 2 + γ 2 ) − i ( α β + γ δ ) β δ − α γ i ( α γ + β δ ) α δ + β γ ] {\displaystyle R(\alpha ,\beta ,\gamma ,\delta )={\begin{bmatrix}{\frac {1}{2}}(\alpha ^{2}-\gamma ^{2}+\delta ^{2}-\beta ^{2})&{\frac {i}{2}}(\gamma ^{2}-\alpha ^{2}+\delta ^{2}-\beta ^{2})&\gamma \delta -\alpha \beta \\{\frac {i}{2}}(\alpha ^{2}+\gamma ^{2}-\beta ^{2}-\delta ^{2})&{\frac {1}{2}}(\alpha ^{2}+\gamma ^{2}+\beta ^{2}+\gamma ^{2})&-i(\alpha \beta +\gamma \delta )\\\beta \delta -\alpha \gamma &i(\alpha \gamma +\beta \delta )&\alpha \delta +\beta \gamma \end{bmatrix}}}
と表示するものである。