-
Vectors An element of a vector space
o An element of the real coordinate space Rn o Basis vector, one
of a set of vectors (a "basis") that, in linear combination,
can represent every vector in a given vector space o Column
vector or row vector, a one-dimensional matrix often
representing
the solution of a system of linear equations o 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.
o Burgers vector, a vector that represents the magnitude and
direction of the lattice distortion of dislocation in a crystal
lattice
o LaplaceRungeLenz vector, a vector used chiefly to describe the
shape and orientation of the orbit of one astronomical body around
another
o Normal vector, or surface normal, a vector that is
perpendicular to a (hyper)surface at a point
o 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 fields Vector field, a construction in vector calculus
that associates a vector to every point
in a subset of Euclidean space o Conservative vector field, a
vector field that is the gradient of a scalar
potential field o Hamiltonian vector field, a vector field
defined for any energy function or
Hamiltonian o Killing vector field, a vector field on a
Riemannian manifold o Solenoidal vector field, a vector field with
zero divergence o 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 o Dual
vector space, a vector space consisting of all linear functionals
on
another, given vector space o Euclidean vector space, an
n-dimensional space with notions of distance and
angle that obey the Euclidean relationships o Graded vector
space, a type of vector space that includes the extra structure
of gradation o Normed vector space, a vector space on which a
norm is defined o Ordered vector space, a vector space equipped
with a partial order o Super vector space, name for a Z2-graded
vector space o Symplectic vector space, a vector space V equipped
with a non-degenerate,
skew-symmetric, bilinear form o 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 , 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
Vectors An element of a vector space
o An element of the real coordinate space Rn o Basis vector, one
of a set of vectors (a "basis") that, in linear combination,
can represent every vector in a given vector space o Column
vector or row vector, a one-dimensional matrix often
representing
the solution of a system of linear equations o 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.
o Burgers vector, a vector that represents the magnitude and
direction of the lattice distortion of dislocation in a crystal
lattice
o LaplaceRungeLenz vector, a vector used chiefly to describe the
shape and orientation of the orbit of one astronomical body around
another
o Normal vector, or surface normal, a vector that is
perpendicular to a (hyper)surface at a point
o 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 fields Vector field, a construction in vector calculus
that associates a vector to every point
in a subset of Euclidean space o Conservative vector field, a
vector field that is the gradient of a scalar
potential field
-
o Hamiltonian vector field, a vector field defined for any
energy function or Hamiltonian
o Killing vector field, a vector field on a Riemannian manifold
o Solenoidal vector field, a vector field with zero divergence o
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 o Dual
vector space, a vector space consisting of all linear functionals
on
another, given vector space o Euclidean vector space, an
n-dimensional space with notions of distance and
angle that obey the Euclidean relationships o Graded vector
space, a type of vector space that includes the extra structure
of gradation o Normed vector space, a vector space on which a
norm is defined o Ordered vector space, a vector space equipped
with a partial order o Super vector space, name for a Z2-graded
vector space o Symplectic vector space, a vector space V equipped
with a non-degenerate,
skew-symmetric, bilinear form o 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 , 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
