# Scalar Field

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## scalar field

[′skā·lər ′fēld] (mathematics)

The field consisting of the scalars of a vector space.

A function on a vector space into the scalars of the vector space.

(physics)

A field which is characterized by a function of position and time whose value at each point is a scalar.

## Scalar Field

a region with each of whose points *P* there is associated a number *a(P*) called a scalar. Mathematically, a scalar field can be defined in a given region *G* by specifying a scalar function *a(P*) of each point *P* of the region. Examples of scalar fields are the temperature field in a body and a density field. The methods of vector analysis are used to study scalar fields.