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
Finite real matrix is positive definite iff symmetric part is