[C_3] = 
{\color{red} \langle \vec k_{3L} \vec k_{3L}^{\:\dagger} \rangle }=
\left[ \begin{array}{rrrr}
S_{11} & S_{21} & S_{31} \\
S_{12} & S_{22} & S_{32} \\
S_{13} & S_{23} & S_{33} 
\end{array} \right] 
