The set of proper Lorentz transformations, i.e. rotations in the four-dimensional space x, y, z, τ, where x, y, and z are space coordinates and τ = ict, where t is the time and c is the speed of light in a vacuum. The Lorentz group is named after H. A. Lorentz. If the Lorentz group is combined with translations in space and time the proper Poincaré group is formed; this is named after the French mathematician and scientist Henri Poincaré (1854–1912). If inversions in space and time are combined with the proper Poincaré group the unrestricted Poincaré group results. Analysis of the Lorentz group in relativistic quantum mechanics is used to classify elementary particles.