\begin{equation}
\left.\begin{gathered}
S_{11}=\sqrt{a_{11}},\quad S_{21}=\frac{a_{12}}{\sqrt{a_{11}}},\quad S_{31}=\frac{a_{13}}{\sqrt{a_{11}}},\\
S_{22}=\sqrt{a_{22}-S_{21}^{2}},\quad S_{32}=\left(a_{23}-\frac{a_{12}}{\sqrt{a_{11}}}\frac{a_{13}}{\sqrt{a_{11}}}\right)\frac{1}{\sqrt{a_{22}-S_{21}^2}},\\
S_{33}=\sqrt{a_{33}-S_{31}^{2}-S_{32}^2}.
\end{gathered}\right\}
\end{equation}