 Solution

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/a/solution

R \in SO (3)

T_{ijk l}^{'} = R_{ia} R_{jb} R_{k c} R_{l d} T_{ab c d} .

An isotropic tensor is unchanged under every such rotation, so its components satisfy

T_{ijk l} = R_{ia} R_{jb} R_{k c} R_{l d} T_{ab c d}

for every

R \in SO (3)

. The repeated indices are summed by the Einstein summation convention.

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