Editing Lorentz transformation (section)

=== Inhomogeneous Lorentz group ===

Two other spacetime symmetries have not been accounted for. In order for the spacetime interval to be invariant, it can be shown<ref>{{harvnb|Weinberg|1972}}</ref> that it is necessary and sufficient for the coordinate transformation to be of the form
<math display="block">X' = \Lambda X + C </math>
where ''C'' is a constant column containing translations in time and space. If ''C'' ≠ 0, this is an '''inhomogeneous Lorentz transformation''' or '''[[Poincaré transformation]]'''.<ref>{{harvnb|Weinberg|2005|pages=55–58}}</ref><ref>{{harvnb|Ohlsson|2011|page=3–9}}</ref> If ''C'' = 0, this is a '''homogeneous Lorentz transformation'''. Poincaré transformations are not dealt further in this article.