vektoriellen

Vektoriellen is a term found in several Nordic languages as the definite form of the adjective meaning vector-related or pertaining to vectors. It is used to describe nouns that involve vectors, vector quantities, or vector-valued concepts in mathematics, physics, and engineering. In practice, the base form vektoriell (or a closely related form) carries the general meaning “vectorial,” while vektoriellen marks definiteness in a noun phrase.

Etymology and morphology are typical of Germanic languages, where a root meaning vector is combined with an adjective suffix meaning “pertaining to.” The definite form is created through language-specific inflection, resulting in a form like vektoriellen when referring to a specific vector-related concept.

In mathematical and scientific usage, vektoriell concepts describe objects that can be represented by vectors. This includes vector spaces, where elements are vectors; vector fields, which assign a vector to every point in a region; and vector-valued functions, which map inputs to vectors. Operations such as vector addition, scalar multiplication, and basis representations are described using the same vector-centric vocabulary that underlies the broader term vektoriell. In physics and engineering, vektoriellen descriptors appear in discussions of velocity, force, momentum, and other quantities that have both magnitude and direction.

Because the languages differ in exact spelling and definite-marking, translations of vektoriellen may use language-specific equivalents of “vectorial” or “vector-related,” with the definite form applied according to the grammar of the respective language. See also vector, vector space, vector field, and vector calculus.