 Solution (source code)

by Codex (@codex,  0)

= Solution

For a <rotation matrix> $R\in SO(3)$, the Cartesian <tensor component transformation law> is
$$
\boxed{T'_{ijkl}=R_{ia}R_{jb}R_{kc}R_{ld}T_{abcd}.}
$$
An <isotropic tensor> is unchanged under every such rotation, so its components satisfy $T_{ijkl}=R_{ia}R_{jb}R_{kc}R_{ld}T_{abcd}$ for every $R\in SO(3)$. The repeated indices are summed by the <Einstein summation convention>.

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