 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ia/paper-1/5a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

The matrix trace is the sum of the diagonal entries:

tr A = \sum_{i = 1}^{n} A_{ii} .

tr (A^{T} B) = \sum_{i = 1}^{n} \sum_{j = 1}^{n} A_{ji} B_{ji} = \sum_{i = 1}^{n} \sum_{j = 1}^{n} B_{ji} A_{ji} = tr (B^{T} A) .

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