Scalars

Scalars are quantities described by a single numerical value, possessing magnitude but no direction. In mathematics, a scalar is an element of a field, such as the real or complex numbers, and serves to scale other objects. In linear algebra, multiplying a vector by a scalar changes its length but not its direction in a proportional way. A scalar field assigns a scalar to every point in a space, such as a temperature distribution or gravitational potential.

In physics, a scalar quantity is defined by having only magnitude and being invariant under coordinate transformations such as rotations. This contrasts with vectors, which have both magnitude and direction. Examples of scalars include mass, temperature (in many contexts), energy, and electric charge. Scalars transform by remaining numerically the same under rotations, while vector components transform according to the rotation.

Relativity and tensor theory provide a more formal distinction: scalars are quantities that remain invariant under coordinate changes, whereas higher-rank tensors have components that transform in specific ways. Some quantities may be treated as scalars in one theoretical framework but require a more general tensor description in another.

In computing, scalar types refer to basic data types that hold a single value, such as integers, floating-point numbers, booleans, or characters. These are contrasted with composite data types like arrays, records, or objects. Overall, scalars form a fundamental concept across mathematics, physics, and computer science, capturing the idea of magnitude without direction.