Lorentz transformations form a group ↩

aliases: []
shorthands: {}
created: 2022-02-22 18:45:14
modified: 2022-02-22 18:57:31

Proof

Let's denote the transformations with and the corresponding matrices with and check the group axioms:

• (A0) Lorentz transformations is a Lorentz transformation as well?
  We just check the well known defining identity:

• (A1) Associativity is given, since the matrices that represent the transformations (linear transformations) are associative
• (A2) The neutral element corresponds to the identity matrix
• (A3) All Lorentz transformations have an inverse, since the matrices have a non-zero determinant, so are invertible

QED