Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 4C / b / Solution

For the special-relativistic matrix,Thus the eigenvalues and corresponding eigenvectors areThe eigenvector equations are $x=ct$ and $x=-ct$. They are the two null directions of the light cone, representing right-moving and left-moving light rays. A Lorentz boost preserves each light-ray direction while rescaling its null coordinate.