vektorial

Vektorial is an adjective used in mathematics, physics and related fields to indicate a relation to vectors or vector-valued quantities. In everyday mathematical usage, a vector is an object that has both magnitude and direction, as opposed to scalars which have only magnitude. Vektorial describes properties, operations or objects that involve vectors or vector fields.

In linear algebra, vectorial objects include vectors in a vector space, linear combinations, and linear transformations. Many problems consider vector-valued functions, where a single input maps to a vector output, such as position as a function of time or velocity as a function of space.

In calculus and physics, vector fields assign a vector to every point in a space. Examples include a velocity field describing how fast and in which direction fluid particles move, or a force field assigning a force vector throughout a region. Operations on vector fields include addition, scalar multiplication, divergence and curl, which are inherently vectorial.

From a geometric standpoint, vektorial emphasizes direction and orientation. When working in coordinates, a vector is often represented by an ordered list of numbers (components) relative to a chosen basis, enabling computations of dot products, cross products, projections and norms.

In computer science and numerical simulations, vectorization or vektorial representations refer to data structures and algorithms that manipulate collections of vectors efficiently, such as arrays of coordinate vectors or vector fields in simulations.

Understanding whether a quantity is vectorial helps determine the appropriate rules for combining and transforming it, and clarifies whether magnitude or direction plays the essential role.

See also: vector, vector field, linear algebra, vector calculus, scalar.