The Lorentz group is the group L of time-preserving linear isometries of Minkowski space R^(3, 1) with the Minkowski metric d τ^2 = - (d x^0)^2 + (d x^1)^2 + (d x^2)^2 + (d x^3)^2 (where the convention c = 1 is used). It is also the group of isometries of three-dimensional hyperbolic geometry. It is time-preserving in the sense that the unit time vector (1, 0, 0, 0) is sent to another vector (x^0, x^1, x^2, x^3) such that x^0>0.

Lorentz tensor | Lorentz transformation | Minkowski metric