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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/6/c/i/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2025 / Paper 2 / 6 / c / i / Solution by

Codex  0 2026-10-18

Relabel the two dummy indices and use the respective symmetries:

X_{ij} A_{ij} = X_{ji} A_{ji} = - X_{ij} A_{ij} = 0.

Thus the symmetric tensor and antisymmetric tensor subspaces are orthogonal in the Frobenius inner product.

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