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Positive operator

In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operatorA{\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)}, ⟨Ax,x⟩∈R{\displaystyle \langle Ax,x angle \in \mathbb {R} } and ⟨Ax,x⟩≥0{\displaystyle \langle Ax,x angle \geq 0}, where Dom⁡(A){\displaystyle \operatorname {Dom} (A)} is the domain of A{\displaystyle A}.

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