4.2e Positive Semidefinite Matrix

Positive Semidefinite Matrices

A real symmetric matrix $A\in S^n$ is said to be positive semidefinite, denoted as $A⪰0$, if the associated quadratic form is non-negative such that for all $x\in {\mathbb{R}}^n$,
$x^{T}Ax\ge 0.$