ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11690 on D4938: Positive definite real matrix
F11690
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}