Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 3 / 12B / iii

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- Solution iii

Solution

A tensor is isotropic tensor if its components are unchanged under every proper orthogonal change of basis. The general isotropic rank-four tensor is

T_{ijk l} = a δ_{ij} δ_{k l} + b δ_{ik} δ_{j l} + c δ_{i l} δ_{jk},

where

a, b, c

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