Vetoriais

Vetoriais is a term used in Portuguese to refer to objects or quantities described by vectors or that vary as vectors. In mathematical contexts, vetoriais denote elements of a vector space or vector-valued functions, and they form the basis of vector calculus and linear algebra.

Definition: A vetorial quantity is any entity that can be described by a magnitude and a direction or by a vector-valued function. Common examples include displacement, velocity, acceleration, force, and electric field. In more abstract terms, a vetorial object is an element v of a vector space V, supporting addition and scalar multiplication.

Coordinate representation: Vetoriais can be expressed in components relative to a basis. If V has basis e1,...,en, a vector v is written as v = sum vi ei, with components vi. Linear transformations map vetoriais to vetoriais, preserving vector structure.

Types: Vector fields assign a vector to every point in a space (e.g., a velocity field in fluid dynamics). Random vectors extend the idea to probability, mapping outcomes to vectors in R^n.

Applications: Vetoriais are central in physics, engineering, computer graphics, statistics, and data science. They enable compact representation of multi-dimensional data, transformations, and physical laws expressed in vector form.

See also: Scalar, Vector, Vector space, Vector field, Linear transformation, Matrix.

If the term is used in non-technical contexts, it may denote any quantity describing both magnitude and direction or any vector-valued entity.