Positive operator

'''Definition:''' Given a [[Hilbert space]] $\backslash ;\; \backslash mathcal\{H\}$ and $\backslash ;\; A\; \backslash in\; L(\backslash mathcal\{H\})$, $\backslash ;\; A$ is said to be a '''positive operator''' if $\backslash ;\; \backslash langle\; A\; x,\; x\; \backslash rangle\; \backslash ge\; 0$ for every $\backslash ;\; x\; \backslash in\; \backslash mathcal\{H\}$. A positive operator on a complex Hilbert space is necessarily a [[symmetric operator]] and has a self-adjoint extension that is also a positive operator. The set of positive bounded operators on a Hilbert space forms a cone in the algebra of all bounded operators. [[Category:Mathematical Structure]] [[Category:Linear Algebra]] {{stub}}