In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under...

particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart...

spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle...

An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric...

charge per unit time per unit area. Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than separating...

a wave four-vector can be defined, combining the (angular) wave vector and (angular) frequency. The terms wave vector and angular wave vector have distinct...

operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is...

the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity...

In differential geometry, the four-gradient (or 4-gradient) ∂ {\displaystyle {\boldsymbol {\partial }}} is the four-vector analogue of the gradient ∇ →...

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...

four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see...

In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:...

The four-frequency of a massless particle, such as a photon, is a four-vector defined by N a = ( ν , ν n ^ ) {\displaystyle N^{a}=\left(\nu ,\nu {\hat...

electromagnetic four-potential is a covariant four-vector containing the electric potential (also called the scalar potential) ϕ and magnetic vector potential...

transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates. If A is any four-vector, then in tensor index notation A...

potential and the magnetic vector potential. The electric potential and the magnetic vector potential together form a four-vector, so that the two kinds of...

quantity to a spacelike vector quantity, and we have 4d vectors, or "four-vectors", in Minkowski spacetime. The components of vectors are written using tensor...

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space....

perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's...

of relativity, four-force is a four-vector that replaces the classical force. The four-force is defined as the rate of change in the four-momentum of a...

In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field...

spacetime represented as a four-vector (t, x, y, z). A Lorentz transformation is represented by a matrix that acts on the four-vector, changing its components...

For instance, many times the time-based terms are placed first in the four-vectors, with the spatial terms following. Also, sometimes η is replaced with...

listed next. In special relativity, the vector basis can be restricted to being orthonormal, in which case all four-tensors transform under Lorentz transformations...

of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e...

coordinates combine into the four-position, and energy and momentum combine into the four-momentum. The components of these four-vectors depend on the frame of...

object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then...

momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's...

Poincaré group (the inhomogeneous Lorentz group). Thus, a is a real Lorentz four-vector representing the change of spacetime origin x ↦ x − a, where x is in...

example of a bilinear form that is not an inner product would be the four-vector product. The definition of a bilinear form can be extended to include...