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Positive definite real matrix
Formulation 0
A D6160: Real square matrix $A \in \mathbb{R}^{N \times N}$ is positive definite if and only if \begin{equation} \forall \, x \in \mathbb{R}^{N \times 1} \setminus \{ \boldsymbol{0} \} : x^T A x \in (0, \infty) \end{equation}
Results
» R3748: Finite real matrix is positive definite iff symmetric part is