= Directional elastic strain Green operator
{title2=$\widetilde\Gamma_C(n)=B_n(B_n^TCB_n)^{-1}B_n^T$}
Let $B_na=\operatorname{sym}(a\otimes n)$; its adjoint on symmetric <stress tensors> is $B_n^T\tau=\tau n$. Then $B_n^TCB_n$ is the <acoustic tensor>. The <directional elastic strain Green operator> satisfies the resolvent identity $\widetilde\Gamma_r(C^r-C^s)\widetilde\Gamma_s=\widetilde\Gamma_s-\widetilde\Gamma_r$, by the elementary inverse identity $K_r^{-1}(K_r-K_s)K_s^{-1}=K_s^{-1}-K_r^{-1}$.
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