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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…

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Application to physics: quantum states

Quantum systemSeparable Hilbert spaceTrace-classOperatorsSet
9 related topics

Partial order of self-adjoint operators

Partial orderingMonotone convergence theoremMonotone increasing
3 related topics

Overview

MathematicsLinear algebraOperator theoryFunctional analysisPhysics
12 related topics

On a complex Hilbert space, if an operator is non-negative then it is symmetric

Polarization identityAcute angle
2 related topics

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Cauchy–Schwarz inequality

On a complex Hilbert space, if an operator is non-negative then it is symmetric

If an operator is non-negative and defined on the whole complex Hilbert space, then it is self-adjoint and bounded

Partial order of self-adjoint operators

Application to physics: quantum states

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Positive operator

Nodes36
Edges35
Triples6
Avg. degree1.94
Density0.055556
Components1

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Positive operator

Top relations

related to On a complex Hilbert space, if an operator is non-negative then it is symmetric · 4
Positive operator → Ax, Ay, Dom, For
related to Partial order of self-adjoint operators · 2
Positive operator → B-A, Define

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displaystyle operator operators mathbb space hilbert dom langle ax rangle self-adjoint symmetric complex states physics operatorname positive non-negative called define

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SubjectPredicateObjectConfidenceSrc
Positive operatorrelated to On a complex Hilbert space, if an operator is non-negative then it is symmetricFor0.60section
Positive operatorrelated to On a complex Hilbert space, if an operator is non-negative then it is symmetricDom0.60section
Positive operatorrelated to On a complex Hilbert space, if an operator is non-negative then it is symmetricAx0.60section
Positive operatorrelated to On a complex Hilbert space, if an operator is non-negative then it is symmetricAy0.60section
Positive operatorrelated to Partial order of self-adjoint operatorsDefine0.60section
Positive operatorrelated to Partial order of self-adjoint operatorsB-A0.60section

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