Skalär

In mathematics and physics, skalær (scalar) is a quantity described by a single magnitude, with no directional component. It contrasts with vectors, which have both magnitude and direction, and with tensors of higher rank. A skalær is typically associated with a scalar field; its values belong to a scalar field, commonly the real numbers or complex numbers.

Examples include mass, temperature, time interval, energy, electric charge, and distance. In general, a skalær can be added to other scalars and multiplied by real or complex numbers, and these operations obey ordinary arithmetic.

A key property is that the value of a skalær does not depend on the orientation of the coordinate system. When used in physics, distinguishing scalar quantities from vector quantities helps describe physical phenomena: speed is a skalær, while velocity is a vector.

Scalar fields are functions that assign a skalær to every point in space, such as a temperature field defined over a region. In calculus, many physical quantities arise as the result of dot products or contractions, producing scalars.

In relativistic contexts, some scalars are invariant under coordinate transformations; for instance, a real-valued density can be treated as a scalar. In general linear algebra, a scalar is an element of the underlying field, used to scale vectors and matrices.