**Minkowski space** is 4-dimensional quasi-Euclidean space (i.e., the set of points ) together with the metric:

It is called quasi-Euclidean because the metric coefficients for space and time are different, rather than always being positive for a true Euclidean space. Whether the time coefficient or the space coefficients should be the negative ones has been debated for a century. It doesn't matter in practice. The convention above (time is positive and space negative) was the one preferred by Einstein.

A vector *v* in Minkowski space is said to be time-like if , light-like if and space-like if . The isometries of Minkowski space are the Lorentz transformations.

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