ベクトル場の回転

$\displaystyle \mathrm{rot} \{ b \}$	$\textstyle =$	$\displaystyle \{ \nabla \} \times \{ b \}$
	$\textstyle =$	$\displaystyle \frac{ \partial b_i }{ \partial x_j } e_{jik} \{ e \} _k$
	$\textstyle =$	$\displaystyle \left\{ \begin{array}{c} \frac{ \partial b_2 }{ \partial x_1 } - ... ... }{ \partial x_0 } - \frac{ \partial b_0 }{ \partial x_1 } \end{array} \right\}$
	$\textstyle =$	$\displaystyle \left\{ \begin{array}{c} \frac{ \partial b_z }{ \partial y } - \f... ... b_y }{ \partial x } - \frac{ \partial b_x }{ \partial y } \end{array} \right\}$	(2.168)

$\displaystyle \mathrm{rot} \{ b \}$	$\textstyle =$	$\displaystyle \{ b \} \times \{ \nabla \}$
	$\textstyle =$	$\displaystyle \frac{ \partial b_i }{ \partial x_j } e_{ijk} \{ e \} _k$
	$\textstyle =$	$\displaystyle \left\{ \begin{array}{c} \frac{ \partial b_1 }{ \partial x_2 } - ... ... }{ \partial x_1 } - \frac{ \partial b_1 }{ \partial x_0 } \end{array} \right\}$
	$\textstyle =$	$\displaystyle \left\{ \begin{array}{c} \frac{ \partial b_y }{ \partial z } - \f... ... b_x }{ \partial y } - \frac{ \partial b_y }{ \partial x } \end{array} \right\}$	(2.169)

一般に、前形（左形） $\{ \nabla \} \times \{ b \}$ が用いられることが多い。