Full set of all possible special relativity symmetries:

- translations in space and time
- rotations in space
- Lorentz boosts

In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.

There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.

- space and time shifts, because their space origin and time origin (time they consider 0, i.e. when they started their timers) are not synchronized. This can be modelled with a 4-vector addition.
- their space axes are rotated relative to one another. This can be modelled with a 4x4 matrix multiplication.
- and they are moving relative to each other, which leads to the usual spacetime interactions of special relativity. Also modelled with a 4x4 matrix multiplication.

The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.

- Important Lie groups | 0, 693, 13
- Lie group | 198, 1k, 19
- Important mathematical groups | 0, 1k, 25
- Group | 0, 2k, 47
- Algebra | 0, 2k, 65
- Mathematics | 17, 10k, 239
- Ciro Santilli's Homepage | 238, 147k, 2k

- Lorentz group | 61, 103, 2
- Lecture 1 | 240