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Positive definite complex matrix
Formulation 0
A D6159: Complex square matrix $A \in \mathbb{C}^{N \times N}$ is positive definite if and only if \begin{equation} \forall \, z \in \mathbb{C}^{N \times 1} \setminus \{ \boldsymbol{0} \} : z^* A z \in (0, \infty) \end{equation}