行列式
$ f:=\begin{pmatrix}f_1(x_1,\dots,x_n) \\ \vdots \\ f_m(x_1,\dots,x_n)\end{pmatrix}に對して$ J_f:=\frac{\partial f}{\partial{\bf x}}=\begin{pmatrix}\frac{\partial f_1}{\partial x_1} & \dots & \frac{\partial f_1}{\partial x_n} \\ \vdots & \ddots & \vdots \\ \frac{\partial f_m}{\partial x_1} & \dots & \frac{\partial f_m}{\partial x_n}\end{pmatrix}.
Jacobian$ |J_f|(Jacobian 行列式)
$ f(x_1,\dots,x_n)に對して$ H(f):=\nabla\otimes\nabla f=\begin{pmatrix}\frac{\partial^2 f}{\partial x_1\partial x_1} & \dots & \frac{\partial^2 f}{\partial x_1\partial x_n} \\ \vdots & \ddots & \vdots \\ \frac{\partial^2 f}{\partial x_n\partial x_1} & \dots & \frac{\partial^2 f}{\partial x_n\partial x_n}\end{pmatrix}
Hessian$ |H(f)|(Hessian 行列式)