vektoriell

Vektoriell is an adjective used in Norwegian and Swedish to describe things related to vectors. In English, the closest translations are vectorial or vector-valued. The term signals that a quantity, object, or property is defined by, or attached to, vectors rather than scalars.

In mathematics, vektoriell typically refers to vector-valued objects. Examples include vector-valued functions, which assign a vector to each point in a domain, and vector fields, which assign a vector to every point in a space. A function such as f(t) = (x(t), y(t), z(t)) is described as vektoriell, since its outputs are vectors. Vector fields, like a velocity field in fluid dynamics, are also described as vektoriell because they produce vectors at each spatial point.

In linear algebra and geometry, vektoriell describes properties and operations that preserve or involve vectors, such as vector addition, scalar multiplication, and linear transformations represented by matrices. In analysis, vector calculus studies vector-valued functions and vector fields, employing operators like gradient, divergence, and curl. These concepts illustrate how vektoriell objects behave under differentiation and integration in multiple dimensions.

In physics and engineering, many quantities are vector-valued, including velocity, force, and electric or magnetic fields. Distinguishing vektoriell (vector-valued) from scalar quantities helps clarify the nature of physical laws and equations.

The term also appears in computer graphics and data visualization, where vector fields or vector graphics describe images or data in terms of vectors rather than pixels or scalar values. Overall, vektoriell emphasizes a relation to vectors and to mappings or structures that assign vectors, rather than scalar values, to elements of a domain.