6.5 ダイアディック公式
ダイアディックの公式（dyadic identities）をまとめると，次のようになる．
\begin{align}
&\VEC{a} \cdot (\VEC{b} \times \DYA{c} )
= -\VEC{b} \cdot (\VEC{a} \times \DYA{c} )
= (\VEC{a} \times \VEC{b}) \cdot \DYA{c}
\\
&\VEC{a} \times (\VEC{b} \times \DYA{c} )
= \VEC{b} \cdot (\VEC{a} \times \DYA{c} )
- (\VEC{a} \cdot \VEC{b}) \DYA{c}
\\
&\nabla (a \VEC{b})
= a \nabla \VEC{b} + (\nabla a) \VEC{b}
\\
&\nabla \cdot (a \DYA{b})
= a \nabla \cdot \DYA{b} + (\nabla a) \cdot \DYA{b}
\\
&\nabla \times (a \DYA{b})
= a \nabla \times \DYA{b} + (\nabla a) \times \DYA{b}
\\
&\nabla \times (\nabla \times \DYA{a})
= \nabla ( \nabla \cdot \DYA{a}) + \nabla^2 \DYA{a}
\\
&\nabla \cdot (\nabla \times \DYA{a}) = 0
\\
&\VEC{a} \cdot \DYA{b} = (\DYA{b})^T \cdot \VEC{a}
\\
&\VEC{a} \times \DYA{b} = - \left[ (\DYA{b})^T \times \VEC{a} \right]^T
\\
&(\DYA{c})^T \cdot (\VEC{a} \times \DYA{b})
= - (\VEC{a} \times \DYA{c} )^T \cdot \DYA{b}
\end{align}