When used without any further description, vector refers either to:
Most generally, an element of a vector space
In physics and geometry, a Euclidean vector, used to represent physical quantities that have both magnitude and direction
Vector can also have a variety of different meanings depending on context.
An element of a vector space
An element of the real coordinate space Rn
Basis vector, one of a set of vectors (a "basis") that, in linear combination, can represent every vector in a given vector space
Column vector or row vector, a one-dimensional matrix often representing the solution of a system of linear equations
Coordinate vector, in linear algebra, an explicit representation of an element of any abstract vector space
Axial vector, or pseudovector, a quantity that transforms like a vector under proper rotation but not generally under reflection
Darboux vector, the areal velocity vector of the Frenet frame of a space curve
Displacement vector, a vector that specifies the change in position of a point relative to a previous position
Euclidean vector, a geometric entity endowed with magnitude and direction as well as a positive-definite inner product; an element of a Euclidean vector space. In physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, such as force, in contrast to scalar quantities, which have no direction.
Burgers vector, a vector that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice
Laplace–Runge–Lenz vector, a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another
Normal vector, or surface normal, a vector that is perpendicular to a (hyper)surface at a point
Vector product, or cross product, an operation on two vectors in a three-dimensional Euclidean space, producing a third three-dimensional Euclidean vector
Four-vector, in the theory of relativity, a vector in a four-dimensional real vector space called Minkowski space
Gradient vector, the vector giving the magnitude and direction of maximum increase of a scalar field
Gyrovector, a hyperbolic geometry version of a vector
Interval vector, in musical set theory, an array that expresses the intervallic content of a pitch-class set
Null vector, a vector whose magnitude is zero
P-vector, the tensor obtained by taking linear combinations of the wedge product of p tangent vectors
Position vector, a vector representing the position of a point in an affine space in relation to a reference point
Poynting vector, in physics, a vector representing the energy flux density of an electromagnetic field
Probability vector, in statistics, a vector with non-negative entries that sum to one
Random vector or multivariate random variable, in statistics, a set of real-valued random variables that may be correlated
Spin vector, or Spinor, is an element of a complex vector space introduced to expand the notion of spatial vector
Tangent vector, an element of the tangent space of a curve, a surface or, more generally, a differential manifold at a given point.
The vector part of a quaternion, a mathematical entity that is one possible generalisation of a vector
Tuple, an ordered list of numbers, sometimes used to represent a vector
Unit vector, a vector in a normed vector space whose length is 1
Wave vector, a vector representation of the local phase evolution of a wave
Vector field, a construction in vector calculus that associates a vector to every point in a subset of Euclidean space
Conservative vector field, a vector field that is the gradient of a scalar potential field
Hamiltonian vector field, a vector field defined for any energy function or Hamiltonian
Killing vector field, a vector field on a Riemannian manifold
Solenoidal vector field, a vector field with zero divergence
Vector potential, a vector field whose curl is a given vector field
Vector flow, a set of closely related concepts of the flow determined by a vector field
Vector space, a mathematical structure made up of vectors, objects that may be added with another vector or multiplied by a scalar value
Dual vector space, a vector space consisting of all linear functionals on another, given vector space
Euclidean vector space, an n-dimensional space with notions of distance and angle that obey the Euclidean relationships
Graded vector space, a type of vector space that includes the extra structure of gradation
Normed vector space, a vector space on which a norm is defined
Ordered vector space, a vector space equipped with a partial order
Super vector space, name for a Z2-graded vector space
Symplectic vector space, a vector space V equipped with a non-degenerate, skew-symmetric, bilinear form
Topological vector space, a blend of topological structure with the algebraic concept of a vector space
Manipulation of vectors, fields, and spaces
Vector Analysis, a textbook on vector calculus by Wilson, first published in 1901, which did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus
Vector bundle, a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
Vector calculus, a branch of mathematics concerned with differentiation and integration of vector fields
Vector decomposition, a technique to convert a vector of Rn into several vectors, each linearly independent
Vector differential, or del, a vector differential operator represented by the nabla symbol
∇
Vector Laplacian, the vector Laplace operator, denoted by
∇
2
, is a differential operator defined over a vector field
Vector notation, common notation used when working with vectors
Vector operator, a type of differential operator used in vector calculus
Vector product, or cross product, an operation on two vectors in a three-dimensional Euclidean space, producing a third three-dimensional Euclidean vector
Vector projection, also known as vector resolute or vector component, a linear mapping producing a vector parallel to a second vector
Vector-valued function, a mathematical function that maps real numbers to vectors
Vectorization (mathematics), a linear transformation that converts a matrix into a column vector
Other uses in mathematics and physics
Vector autoregression, an econometric model used to capture the evolution and the interdependencies between multiple time series
Vector boson, a boson with the spin quantum number equal to 1
Vector measure, a function defined on a family of sets and taking vector values satisfying certain properties
Vector meson, a meson with total spin 1 and odd parity
Vector quantization, a quantization technique used in signal processing
Vector soliton, a solitary wave with multiple components coupled together that maintains its shape during propagation
Vector synthesis, a type of audio synthesis
Witt vector, an infinite sequence of elements of a commutative ring
Vector (mathematics and physics) Wikipedia (Text) CC BY-SA