The Galilean transformation is a transformation from one reference frame to another moving with a constant velocity 
with respect to the first for classical motion. However, special
relativity shows that the transformation must be modified to the Lorentz
transformation for relativistic motion. The forward Galilean transformation is
![[t^'; x^'; y^'; z^']=[1 0 0 0; -v 1 0 0; 0 0 1 0; 0 0 0 1][t; x; y; z],](/images/equations/GalileanTransformation/NumberedEquation1.svg) |
and the inverse transformation is
![[t; x; y; z]=[1 0 0 0; v 1 0 0; 0 0 1 0; 0 0 0 1][t^'; x^'; y^'; z^'].](/images/equations/GalileanTransformation/NumberedEquation2.svg) |
