Let $A \in \mathbb{C}^{N \times M}$ be a D999: Complex matrix.
A D1207: Complex number $\sqrt{\lambda} \in \mathbb{C}$ is a principal value for $A$ if and only if
\begin{equation}
\exists \, z \in \mathbb{C}^{M \times 1} \setminus \{ \boldsymbol{0} \} :
A^* A z = \lambda z
\end{equation}