Minkowski space

Minkowski space is 4-dimensional Euclidean space (i.e., the set of points $(x,y,z,t)$) together with the metric:

$c^{2}dt^{2}-dx^{2}-dy^{2}-dz^{2}$

A vector v in Minkowski space is said to be time-like if $||v||^{2}>0$, light-like if $||v||^{2}=0$ and space-like if $||v||^{2}<0$. The isometries of Minkowski space are the Lorentz transformations.