The <special orthogonal group> is
$$
SO(5)=\{R\in GL(5,\mathbb R):R^TR=I,\ \det R=1\}.
$$
Its <Lie algebra> consists of antisymmetric $5\times5$ matrices, determined by the entries above the diagonal. Therefore
$$
D=\binom52=10.
$$

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 302 / 4 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-302/4/a/solution