skalaar

Skalaar is the term used in several languages, including Dutch and certain Nordic languages, for what English speakers call a scalar: a quantity that is fully specified by magnitude and has no direction. In mathematics and physics, scalars belong to a field such as the real numbers or complex numbers, and they remain unchanged under coordinate transformations.

Etymology: The word derives from Latin scalaris, via French scalaire, and entered various languages as skalaar or skalar to denote quantities that are independent of orientation.

Definition and properties: Scalars are contrasted with vectors, which have both magnitude and direction. A scalar combines with other scalars through ordinary arithmetic; it commutes under multiplication and obeys standard algebraic rules. Physical examples include mass, temperature, energy, and time. A scalar value is typically denoted by an italic letter, such as s or t.

Scalar fields: A scalar field assigns a scalar to every point in space, producing a quantity that may vary with location, such as a temperature field.

Applications: Scalars simplify equations in physics, engineering, and computer science, serving as the basic building block for more complex objects like vectors and tensors. The distinction between scalars and vectors is fundamental in linear algebra and calculus.

See also: scalar, scalar field, vector, tensor, magnitude, unit.