Vectors (mathematics and physics)

geometric object that has magnitude (or length) and direction

the basic algebraic structure of linear algebra; a module over a field, such that its elements can be added together or scaled by elements of the field

common mnemonic for understanding orientation of axes in three-dimensional space

vector of length one

measure of directional energy flux

number of vectors in any basis of the vector space

theorem in vector calculus

In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components, which transform under Lorentz transformations with respect to a change of basis. Its magnitude is determined by an indefinite quadratic form, the preservation of which defines the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another reference frame).

element of a vector space

vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star

function valued in a vector space; typically a real or complex one

thumb|right|A loop of wire (black), carrying a electric current|current I, creates a [[magnetic field B (blue). If the position and current of the wire are reflected across the plane indicated by the dashed line, the magnetic field it generates would not be reflected: Instead, it would be reflected and reversed. The position and current at any point in the wire are "true" vectors, but the magnetic field B is a pseudovector.]]

geometry problem

manner in which a geometric object varies with a change of basis

Cosines of the angles between the vector and the three coordinate axes.

vector characterising a dislocation in a crystal lattice

physical quantity that is a vector

vector tangent to a curve or surface at a given point

in celestial mechanics, a dimensionless vector with direction pointing from apoapsis to periapsis

linear algebra

linear algebra

Concept in 3-dimensional geometry

property of parallel segments that have the same length and the same direction

vector with non-negative entries that add up to one