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- \begin{equation}
- F(\mathbf{X}_{d})= \left[ \begin{smallmatrix}
- 0 & k_{1}\omega_{d3} & k_{1}\omega_{d2} & ... \\
- k_{2}\omega_{d3} & 0 & k_{2}\omega_{d1} & ...\\
- k_{3}\omega_{d2} & k_{3}\omega_{d1} & 0 & ...\\
- \frac{1}{4}(1+\sigma_{d1}^{2}-\sigma_{d2}^{2}-\sigma_{d3}^{2}) &
- \frac{1}{2}(\sigma_{d1}\sigma_{d2}-\sigma_{d3}) &
- \frac{1}{2}(\sigma_{d1}\sigma_{d3}+\sigma_{d2}) & ... \\
- \frac{1}{2}(\sigma_{d2}\sigma_{d1}+\sigma_{d3}) &
- \frac{1}{4}(1+\sigma_{d2}^{2}-\sigma_{d3}^{2}-\sigma_{d1}^{2}) &
- \frac{1}{2}(\sigma_{d2}\sigma_{d3}-\sigma_{d1}) & ...\\
- \frac{1}{2}(\sigma_{d1}\sigma_{d3}-\sigma_{d2}) &
- \frac{1}{2}(\sigma_{d2}\sigma_{d3}+\sigma_{d1}) &
- \frac{1}{4}(1+\sigma_{d3}^{2}-\sigma_{d1}^{2}-\sigma_{d2}^{2}) & ...\\
- \end{smallmatrix} \right.
- \end{equation}
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