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
Definition D4937
Positive semidefinite real matrix
Formulation 0
A D6160: Real square matrix $A \in \mathbb{R}^{N \times N}$ is positive semidefinite if and only if \begin{equation} \forall \, x \in \mathbb{R}^{N \times 1} : x^T A x \in [0, \infty) \end{equation}
Children
Positive definite real matrix
Results
Real matrix gramians are positive semidefinite