Minkowski space
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Minkowski space is 4-dimensional Euclidean space (i.e., the set of points <math>(x,y,z,t)</math>) together with the metric:
<math> c^2dt^2-dx^2-dy^2-dz^2 </math>
A vector v in Minkowski space is said to be time-like if <math>||v||^2 > 0</math>, light-like if <math>||v||^2 = 0</math> and space-like if <math>||v||^2 < 0</math>. The isometries of Minkowski space are the Lorentz transformations.