Definition 2.1.3.label Let $H$ be a Hilbert space and $T: D(T) \to H$ be a symmetric linear map, then $T$ is semipositive if $\dpb{x, Tx}H \ge 0$ for all $x \in H$, positive if $\dpb{x, Tx}H > 0$ for all $x \in H$, and coercive if there exists $\eps > 0$ such that $\dpb{x, Tx}H \ge \eps \norm{x}_{H}$ for all $x \in H$.