ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Countable map
▼ Array
▼ Matrix
▼ Matrix transpose
▼ Symmetric matrix
▼ Matrix quadratic form
▼ Positive semidefinite complex matrix
▼ Positive semidefinite real matrix
Definition D4938
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