In mathematics and physics, vector can refer to:
Euclidean vector, a geometric entity endowed with both length and direction; an element of a Euclidean vector space. In physics, euclidean vectors are used to represent physical quantities which have both magnitude and direction, such as force, in contrast to scalar quantities, which have no direction.
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 the vector resolute, a mapping of one vector onto another

The vector part of a quaternion, a term used in 19th century mathematical literature on quaternions
Burgers vector, a vector that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice
Displacement vector, a vector that specifies the change in position of a point relative to a previous position
Gradient vector, one vector in a vector field
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 which is perpendicular to a surface
Null vector, or zero vector, a vector whose components are all zero
Orbital state vectors, which define the state of an orbiting body
Position (vector), a vector which represents the position of an object in space in relation to an arbitrary reference point
Poynting vector, in physics, a vector representing the energy flux of an electromagnetic field
Tangent vector (disambiguation), a vector that follows the direction of a curve or a surface at a given point
Wave vector, a vector representation of a wave
Gyrovector, a hyperbolic geometry version of a vector
Axial vector, or pseudovector, a quantity that transforms like a vector under a proper rotation
Basis vector, one of a set of vectors (a "basis") that, in linear combination, can represent every vector in a given vector space
Coordinate vector, in linear algebra, an explicit representation of an element of any abstract vector space
Darboux vector, the areal velocity vector of the Frenet frame of a space curve
Four-vector, in the theory of relativity, a vector in a four-dimensional real vector space called Minkowski space
Interval vector, in musical set theory, an array that expresses the intervallic content of a pitch-class set
P-vector, the tensor obtained by taking linear combinations of the wedge product of p tangent vectors
Probability vector, in statistics, a vector with non-negative entries that add up to one
Row vector or column vector, a one-dimensional matrix often representing the solution of a system of linear equations
Spin vector, or Spinor, is an element of a complex vector space introduced to expand the notion of spatial 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
Vector, an element of a vector space
Vector fields
Vector field, a construction in vector calculus which associates a vector to every point in a subset of Euclidean space
Conservative vector field, a vector field which 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

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Vector spaces
Vector space, a mathematical structure made up of vectors, objects which may be added with another vector or multiplied by a scalar value
Euclidean vector space, an n-dimensional space with notions of distance and angle that obey the Euclidean relationships
Dual vector space, a vector space consisting of all linear functionals on another, given vector space
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 bundle, a topological construction which 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 Analysis, a free, online book on vector calculus first published in 1901 by Edwin Bidwell Wilson
Vector decomposition, refers to decomposing a vector of Rn to several vectors, each linearly independent
Vector differential, or del, is 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 notations 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 the vector resolute, a mapping of one vector onto another
Vector-valued function, a mathematical function that maps real numbers to vectors
Vectorization (mathematics), a linear transformation which 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


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