Introduction to Vectors 11

In mathematics, vector algebra may mean:

Linear algebra, specifically the basic algebraic operations of vector addition and scalar multiplication; see vector space.
The algebraic operations in vector calculus, namely the specific additional structure of vectors in 3-dimensional Euclidean space {\displaystyle \mathbf {R} ^{3}} \mathbf{R}^3 of dot product and especially cross product. In this sense, vector algebra is contrasted with geometric algebra, which provides an alternative generalization to higher dimensions.
Original vector algebras of the nineteenth century like quaternions, tessarines, or coquaternions, each of which has its own product. The vector algebras biquaternions and hyperbolic quaternions enabled the revolution in physics called special relativity by providing mathematical models.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 and 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