Vector (mathematics and physics)
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When used without any further description, vector usually refers either to:
 In physics and geometry, a Euclidean vector is used to represent physical quantities that have both magnitude and direction
 An element of a vector space
 An element of a vector field
Vector can also have a variety of different meanings depending on context.
Vectors
 An element of a vector space
 An element of the real coordinate space R^{n}
 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 onedimensional 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 and a positivedefinite 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 threedimensional Euclidean space, producing a third threedimensional Euclidean vector
 Fourvector, in the theory of relativity, a vector in a fourdimensional 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 pitchclass set
 Null vector, a vector whose magnitude is zero
 Pvector, 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 nonnegative entries that sum to one
 Random vector or multivariate random variable, in statistics, a set of realvalued 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 fields

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 spaces

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 ndimensional 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 Z_{2}graded vector space
 Symplectic vector space, a vector space V equipped with a nondegenerate, skewsymmetric, 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 threedimensional 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 R^{n} 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 , 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 threedimensional Euclidean space, producing a third threedimensional Euclidean vector
 Vector projection, also known as vector resolute or vector component, a linear mapping producing a vector parallel to a second vector
 Vectorvalued 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
See also
Look up vector in Wiktionary, the free dictionary. 
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