 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-4/4c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For the special-relativistic matrix,

A (1 1) = γ (1 - β) (1 1), A (- 1 1) = γ (1 + β) (- 1 1) .

Thus the eigenvalues and corresponding eigenvectors are

λ_{+} = \frac{1 - β}{1 + β}, v_{+} = (1 1), λ_{-} = \frac{1 + β}{1 - β}, v_{-} = (- 1 1) .

x = c t

and

x = - c t

. 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.

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