Galilean coordinate system

A system of coordinates in a pseudo-Euclidean space in which the line element has the form:

$$ds^2=\sum e_idx_i^2,$$

where $e_i=\pm1$. The Galilean coordinate system is analogous to the Cartesian coordinate system in a Euclidean space. The name originates from the applications of the Galilean reference system (cf. Inertial system).