Scalar

A scalar is a quantity described by a single numerical value and is invariant under changes of coordinate system. It has magnitude but no intrinsic direction. This distinguishes it from vectors, which have both magnitude and direction, and from tensors, which transform according to more complex rules.

In mathematics, scalars are elements of a field, typically real or complex numbers, used to scale vectors in a vector space. Scalar multiplication combines a scalar with a vector to produce another vector, and it satisfies distributive, associative, and identity properties. Scalars provide the basic numeric coefficients in linear combinations.

In analysis and physics, scalars can define scalar fields, where a scalar is assigned to every point of a space. Examples include temperature, mass density, and electric potential. Scalar fields enable the computation of derivatives such as gradients and Laplacians, which convey how the field changes in space.

In computer science, scalar types are primitive data types that store single values, such as integers, floating-point numbers, booleans, and characters. They are contrasted with composite data types like arrays and objects. Scalars form the core units of arithmetic, logic, and data representation in programming languages.