| transformation of four-vectors from one inertial frame S to another inertial frame S′ moving in any given direction
Note 1 to entry: General Lorentz transformations form a group. Denoting
the set of all general Lorentz transformations , following rules are fulfilled:
- the identity transformation belongs to ;
- a composition of general Lorentz transformations is associative, i.e.
- to any exists an inverse one such that .
Note 2 to entry: A general Lorentz transformation is a linear, rotational transformation in space-time.
Note 3 to entry: A general Lorentz transformation for synchronized S, S' can be expressed by where
In the case where the representation of four-vectors is given by and their transposition by , then , where is the identity matrix and is a three-dimensional matrix built from the dyadic product of the normalized velocity .
Note 4 to entry: The coherent SI unit of the matrix describing the general Lorentz transformation is one, symbol 1.