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Normal operator

In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon H\rightarrow H} that commutes with its Hermitian adjoint N ∗ {\displaystyle N^{\ast }} , that is: N ∗ N = N N ∗ {\displaystyle N^{\ast }N=NN^{\ast }} .

Products, Properties & Properties in finite-dimensional case

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Properties

Properties in finite-dimensional case

Normal elements of algebras

Generalization

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Normal operator

Nodes40
Edges39
Triples24
Avg. degree1.95
Density0.05
Components1

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Normal operator

Top relations

related to Properties in finite-dimensional case · 11
Normal operator → Hilbert, If, Let PV, Proof, PV, PVT, PVTPV, The, Then, This, TPV
related to Unbounded normal operators · 4
Normal operator → Explicitly, Here, NN, The
related to Generalization · 3
Normal operator → Classes, Hyponormal, The
related to Properties · 3
Normal operator → Let, Normal, The
related to Normal elements of algebras · 2
Normal operator → An, The
is a · 1
Normal operator → orthogonal complement of its range

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Important terminology

normal operator displaystyle operators space theorem orthogonal spectral hilbert ast finite-dimensional product bounded pv self-adjoint case complex inner complement 1h

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Normal operatoris aorthogonal complement of its range0.90text
Normal operatorrelated to GeneralizationThe0.60section
Normal operatorrelated to GeneralizationClasses0.60section
Normal operatorrelated to GeneralizationHyponormal0.60section
Normal operatorrelated to Normal elements of algebrasThe0.60section
Normal operatorrelated to Normal elements of algebrasAn0.60section
Normal operatorrelated to PropertiesNormal0.60section
Normal operatorrelated to PropertiesLet0.60section
Normal operatorrelated to PropertiesThe0.60section
Normal operatorrelated to Properties in finite-dimensional caseIf0.60section
Normal operatorrelated to Properties in finite-dimensional caseHilbert0.60section
Normal operatorrelated to Properties in finite-dimensional caseThis0.60section

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