Two observers O and O’ moving in 3-dimensional space will, according to Galileo’s theory of relativity, have coordinate systems related by

where t, t’ and r, r’ are the time and space coordinates for O, O’, respectively, v is the velocity of O with respect to O’, M is a 3×3 orthogonal, determinant 1 matrix, and c is a constant column vector. In Galileo’s theory, observers agree on the simultaneity of events, the time between events (see time dilation), and the distance between simultaneous events (see Lorentz-Fitzgerald contractions). Compare Lorentz group.