Item
\(\Sigma = \diag(\sigma_1, \sigma_2, \dots, \sigma_n)\) is the diagonal matrix containing the lengths of the principal semiaxes. We order them as
\begin{equation*}
\sigma_1 \geq \sigma_2 \geq \cdots \geq \sigma_n \geq
0.
\end{equation*}
in-context