Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 342 / 3 / b / Solution

DefineBecause $O$ is real orthogonal, the ${\chi }_j$ are again self-adjoint and satisfy the Majorana anticommutation relations. Using $A=O^T\epsilon O$,Each two-dimensional block contributes twice the same ordered bilinear:Henceup to the original additive constant.