Definite Matrix

If I take another Linear Algebra course, I’ll move this file there.

Definition (Positive Definite)

A matrix $M\in {\mathbb{R}}^{n\times n}$ is called positive definite iff $\forall \vec{x}\in {\mathbb{R}}^n,{\vec{x}}^{T}M\vec{x}>0$. We denote this property by $M\succ 0$.

Definition (Positive Semi-definite)

A matrix $M\in {\mathbb{R}}^{n\times n}$ is called positive definite iff $\forall \vec{x}\in {\mathbb{R}}^n,{\vec{x}}^{T}M\vec{x}\ge 0$. We denote this property as $M⪰0$.