A scalar is a quantity specified by a single number or value, as distinct from a vector, matrix, or array, which contain multiple values; it is the simplest form of tensor. Examples of scalars include mass, speed, volume, and temperature.

 

A scalar field is an arrangement of scalar values distributed in a space.

 

Scalar product

The scalar product of two vectors a = (a₁, a₂, a₃) and b = (b₁, b₂, b₃) is the scalar a.b = a_xb_x + a_yb_y + a_zb_z.