Galilean coordinate system

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

$$d{s}^2=\sum e_{i}d{x}_i^2,$$

where $e_i=\pm 1$. 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).