scalärer

Scalärer, called skalär in Swedish (plural skalärer), are quantities described by a single magnitude without a directed component. In mathematics, a scalar is typically an element of a field, usually a real or complex number, that can multiply other objects such as vectors or matrices.

In physics and engineering, a scalar is a quantity that has only magnitude and no direction. Scalars remain unchanged under coordinate transformations, unlike vectors which have both magnitude and direction. Common examples include mass, temperature, energy, time, and electric charge. By contrast, quantities like velocity, force, and displacement are vector quantities.

A related concept is the scalar field, which assigns a scalar value to every point in space. Temperature distributions, gravitational potential, and electric potential are examples of scalar fields. Scalar fields are used to describe spatial variations of scalar quantities across a region.

In mathematics and computer science, scalars are typically real or complex numbers. They serve as the basic units for linear algebra, where they scale vectors and matrices. In programming languages, scalar types include simple data types such as integers, floating-point numbers, and booleans.

Units and dimensions may accompany scalars, but the defining property is lack of direction. This distinguishes scalars from vectors and higher-order tensors, which encode directional information and more complex transformation behaviors. The concept of scalars underpins many areas of science, engineering, and computation.