Field

定義

$\mathbf{F}: S \rightarrow \mathbb{R}^n$

Vector fields are one kind of tensor field.

???

$\mathbf{F}(\mathbf{x}) = \mathbf{0}$

$(f \mathbf{F})(\mathbf{x}) = f(\mathbf{x}) \mathbf{F}(\mathbf{x})$

$\mathbf{(F+G)}(\mathbf{x}) = \mathbf{F}(\mathbf{x}) + \mathbf{G}(\mathbf{x})$

張量場

As a tensor is a generalization of a scalar (a pure number representing a value, like length) and a vector (a geometrical arrow in space), a tensor field is a generalization of a scalar field or vector field that assigns, respectively, a scalar or vector to each point of space.