skalare

Skalare is a term used in several languages to denote scalars, a basic concept in mathematics and physics. A scalar is a quantity described by a single real or complex number, and it has no inherent direction. This distinguishes it from vectors, which require both magnitude and direction, and from tensors, which need multiple components relative to a chosen basis.

Mathematically, scalars participate in ordinary arithmetic: they can be added, subtracted, multiplied, and scaled by other scalars. In most physical theories, scalars are taken from the real numbers, though complex numbers are used in contexts such as quantum mechanics. Scalars form a field, enabling well-defined operations and algebraic structure.

Common examples of scalars include temperature, mass, electric charge, energy, and time. These quantities are fully specified by a magnitude alone. In contrast, a velocity vector would require both speed and direction.

Scalar fields extend the idea by assigning a scalar value to every point in a space or spacetime. Examples include a temperature field T(x) in a room or a gravitational potential field Φ(x). Scalar fields are invariant under many coordinate transformations: the scalar value at a point remains the same regardless of the observer’s orientation or position. (Pseudo-scalars, by contrast, may change sign under certain transformations.)

In computer science, scalars also refer to basic data types that store a single value, as opposed to composite types like arrays or records.

Etymologically, the term scalar derives from Latin scala, meaning scale or ladder, reflecting the notion of measurement along a scale.