ベクトル場の勾配

$\displaystyle \mathrm{grad} \{ b \}$	$\textstyle =$	$\displaystyle \{ \nabla \} \otimes \{ b \}$
	$\textstyle =$	$\displaystyle \frac{ \partial b_j }{ \partial x_i } \{ e \} _i \otimes \{ e \} _j$
	$\textstyle =$	$\displaystyle \left[ \begin{array}{ccc} \frac{ \partial b_0 }{ \partial x_0 } &... ...1 }{ \partial x_2 } & \frac{ \partial b_2 }{ \partial x_2 } \end{array} \right]$
	$\textstyle =$	$\displaystyle \left[ \begin{array}{ccc} \frac{ \partial b_x }{ \partial x } & \... ...l b_y }{ \partial z } & \frac{ \partial b_z }{ \partial z } \end{array} \right]$	(2.165)

$\displaystyle \mathrm{grad} \{ b \}$	$\textstyle =$	$\displaystyle \{ b \} \otimes \{ \nabla \}$
	$\textstyle =$	$\displaystyle \frac{ \partial b_i }{ \partial x_j } \{ e \} _i \otimes \{ e \} _j$
	$\textstyle =$	$\displaystyle \left[ \begin{array}{ccc} \frac{ \partial b_0 }{ \partial x_0 } &... ...2 }{ \partial x_1 } & \frac{ \partial b_2 }{ \partial x_2 } \end{array} \right]$
	$\textstyle =$	$\displaystyle \left[ \begin{array}{ccc} \frac{ \partial b_x }{ \partial x } & \... ...l b_z }{ \partial y } & \frac{ \partial b_z }{ \partial z } \end{array} \right]$	(2.166)

一般に、後形（右形） $\{ b \} \otimes \{ \nabla \}$ が用いられることが多い。