Definition:Scalar Field

Disambiguation

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Scalar Field may refer to:

Scalar Field in context of Linear Algebra

Another term for base field:

Let $\struct {G, +_G, \circ}_K$ be a vector space, where:

$\struct {K, +_K, \times_K}$ is a field

$\struct {G, +_G}$ is an abelian group $\struct {G, +_G}$

$\circ: K \times G \to G$ is a binary operation.

Then the field $\struct {K, +_K, \times_K}$ is called the base field of $\struct {G, +_G, \circ}_K$.

Scalar field in context of Physics

Let $F$ be a field which acts on a region of space $S$.

Let the point-function giving rise to $F$ be a scalar quantity.

Then $F$ is a scalar field.