\documentclass{standalone}
\usepackage{amsmath}
\begin{document}
\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}
\end{document}