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- Projection-valued_measure abstract "In mathematics, particularly in functional analysis, a projection-valued measure (PVM) is a function defined on certain subsets of a fixed set and whose values are self-adjoint projections on a fixed Hilbert space. Projection-valued measures are formally similar to real-valued measures, except that their values are self-adjoint projections rather than real numbers. As in the case of ordinary measures, it is possible to integrate complex-valued functions with respect to a PVM; the result of such an integration is a linear operator on the given Hilbert space.Projection-valued measures are used to express results in spectral theory, such as the important spectral theorem for self-adjoint operators. The Borel functional calculus for self-adjoint operators is constructed using integrals with respect to PVMs. In quantum mechanics, PVMs are the mathematical description of projective measurements. They are generalized by positive operator valued measures (POVMs) in the same sense that a mixed state or density matrix generalizes the notion of a pure state.".
- Projection-valued_measure wikiPageExternalLink ,.
- Projection-valued_measure wikiPageID "1046155".
- Projection-valued_measure wikiPageLength "9764".
- Projection-valued_measure wikiPageOutDegree "45".
- Projection-valued_measure wikiPageRevisionID "660708176".
- Projection-valued_measure wikiPageWikiLink Barry_Simon.
- Projection-valued_measure wikiPageWikiLink Borel_functional_calculus.
- Projection-valued_measure wikiPageWikiLink Borel_set.
- Projection-valued_measure wikiPageWikiLink Category:Linear_algebra.
- Projection-valued_measure wikiPageWikiLink Category:Measures_(measure_theory).
- Projection-valued_measure wikiPageWikiLink Category:Spectral_theory.
- Projection-valued_measure wikiPageWikiLink Complex_measure.
- Projection-valued_measure wikiPageWikiLink Density_matrix.
- Projection-valued_measure wikiPageWikiLink Direct_integral.
- Projection-valued_measure wikiPageWikiLink Function_(mathematics).
- Projection-valued_measure wikiPageWikiLink Functional_analysis.
- Projection-valued_measure wikiPageWikiLink Gerald_Teschl.
- Projection-valued_measure wikiPageWikiLink Hilbert_space.
- Projection-valued_measure wikiPageWikiLink If_and_only_if.
- Projection-valued_measure wikiPageWikiLink Indicator_function.
- Projection-valued_measure wikiPageWikiLink Lp_space.
- Projection-valued_measure wikiPageWikiLink Mathematics.
- Projection-valued_measure wikiPageWikiLink Measurable_function.
- Projection-valued_measure wikiPageWikiLink Measure_(mathematics).
- Projection-valued_measure wikiPageWikiLink Measurement_in_quantum_mechanics.
- Projection-valued_measure wikiPageWikiLink Michael_C._Reed.
- Projection-valued_measure wikiPageWikiLink Observable.
- Projection-valued_measure wikiPageWikiLink POVM.
- Projection-valued_measure wikiPageWikiLink Projection_(linear_algebra).
- Projection-valued_measure wikiPageWikiLink Projection_(mathematics).
- Projection-valued_measure wikiPageWikiLink Quantum_information.
- Projection-valued_measure wikiPageWikiLink Quantum_mechanics.
- Projection-valued_measure wikiPageWikiLink Quantum_state.
- Projection-valued_measure wikiPageWikiLink Ring_homomorphism.
- Projection-valued_measure wikiPageWikiLink Self-adjoint.
- Projection-valued_measure wikiPageWikiLink Self-adjoint_operator.
- Projection-valued_measure wikiPageWikiLink Sigma-algebra.
- Projection-valued_measure wikiPageWikiLink Sigma_additivity.
- Projection-valued_measure wikiPageWikiLink Spectral_theorem.
- Projection-valued_measure wikiPageWikiLink Spectral_theory.
- Projection-valued_measure wikiPageWikiLink Step_function.
- Projection-valued_measure wikiPageWikiLinkText "PVM".
- Projection-valued_measure wikiPageWikiLinkText "Projection-valued measure".
- Projection-valued_measure wikiPageWikiLinkText "Projection-valued_measure".
- Projection-valued_measure wikiPageWikiLinkText "projection-valued measure".
- Projection-valued_measure wikiPageWikiLinkText "projective measurement".
- Projection-valued_measure wikiPageWikiLinkText "projective measurements".
- Projection-valued_measure wikiPageWikiLinkText "spectral resolution".
- Projection-valued_measure date "May 2015".
- Projection-valued_measure reason "Is this a novel term? It's not defined in the linked article.".
- Projection-valued_measure reason "Partition of unity in the operator sense is not defined in the article "partition of unity".".
- Projection-valued_measure reason "What is a measure class? A measure up to measure-preserving equivalence? Should the measure be completed?".
- Projection-valued_measure wikiPageUsesTemplate Template:Clarify.
- Projection-valued_measure subject Category:Linear_algebra.
- Projection-valued_measure subject Category:Measures_(measure_theory).
- Projection-valued_measure subject Category:Spectral_theory.
- Projection-valued_measure hypernym Function.
- Projection-valued_measure type Disease.
- Projection-valued_measure type Algebra.
- Projection-valued_measure comment "In mathematics, particularly in functional analysis, a projection-valued measure (PVM) is a function defined on certain subsets of a fixed set and whose values are self-adjoint projections on a fixed Hilbert space. Projection-valued measures are formally similar to real-valued measures, except that their values are self-adjoint projections rather than real numbers.".
- Projection-valued_measure label "Projection-valued measure".
- Projection-valued_measure sameAs Q339722.
- Projection-valued_measure sameAs Spektralmaß.
- Projection-valued_measure sameAs Medida_espectral.
- Projection-valued_measure sameAs Mesure_spectrale.
- Projection-valued_measure sameAs מידה_הטלתית.
- Projection-valued_measure sameAs Misura_a_valori_di_proiettore.
- Projection-valued_measure sameAs Spectraalmaat.
- Projection-valued_measure sameAs Hermitowska_miara_spektralna.
- Projection-valued_measure sameAs Medida_espectral.
- Projection-valued_measure sameAs m.0417yr.
- Projection-valued_measure sameAs Q339722.
- Projection-valued_measure wasDerivedFrom Projection-valued_measure?oldid=660708176.
- Projection-valued_measure isPrimaryTopicOf Projection-valued_measure.