scalar field

Scalar field

A scalar field is a field that associates a scalar value to every point in space.
It consists of a set $\mathbb{K}$, usually $\mathbb{R}$, and a function $f:{\mathbb{R}}^n\to \mathbb{K}$ that assigns a scalar value to each point in an n-dimensional space.

EXAMPLE

• The temperature distribution in a room can be described by a scalar field, where each point in the room has a specific temperature value.
• Population density across a geographical area can be represented as a scalar field, with each point indicating the number of people per unit area.
• The elevation of terrain in a landscape can be modeled as a scalar field, where each point corresponds to a specific height above sea level.