Positive operator
In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting on an inner product space is called positive-semidefinite (or non-negative) if, for every x ∈ Dom ( A ) {\displaystyle x\in \operatorname {Dom} (A)} , ⟨ A x , x ⟩ ∈ R {\displaystyle \langle Ax,x\rangle \in \mathbb {R} } and ⟨ A x , x ⟩ ≥ 0 {\displaystyle \langle Ax,x\rangle \geq 0} , where Dom ( A ) {\displaystyle \operatorname {Dom} (A)} is the domain of A {\displaystyle A} . Positive-semidefinite operators are denoted as A ≥ 0 {\displaystyle A\geq 0} .