Vektoriale

Vektoriale, or vectorial, is a term used across mathematics, physics and related disciplines to describe concepts, quantities or properties that involve vectors. It denotes a focus on both magnitude and direction rather than solely on size.

In mathematics, a vector is a quantity that has both length and direction. Examples include displacement, velocity and force. The set of all vectors in a given space forms a vector space, equipped with operations of addition and scalar multiplication that satisfy familiar algebraic rules.

A central idea in applied contexts is the vector field: a function that assigns a vector to every point in a region of space. Examples include a velocity field describing the flow of a fluid, or an electric or magnetic field assigning a field vector to each spatial point. Vector fields can be analyzed pointwise or globally using tools from calculus and linear algebra.

Operations on vectors include addition, scalar multiplication, and products that yield scalars or other vectors. The dot product yields a scalar describing the extent of alignment, while the cross product (in three dimensions) yields a vector orthogonal to the plane of the operands. The norm or magnitude of a vector measures its length, and angles between vectors relate to their dot product.

Calculus on vector fields introduces concepts such as the gradient, divergence and curl, which describe rates of change, outflow and rotation, respectively. Linear maps and Jacobians connect vectors and linear transformations, enabling analysis of how vector quantities change with position.

Vektoriale ideas underpin much of physics, engineering, and applied mathematics, including mechanics, electromagnetism, fluid dynamics, and computer graphics.