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Unitary operator

In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Non-trivial examples include rotations, reflections, and the Fourier operator. Unitary operators generalize unitary matrices. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to…

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Definition

Examples

Linearity

Properties

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Unitary operator

Nodes58
Edges57
Triples45
Avg. degree1.97
Density0.034483
Components1

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Unitary operator

Top relations

related to Examples · 26
Unitary operator → Any, Fourier, Givens, Hadamard, Hermitian, Hilbert, Householder, In, More, Not, Notice, On, Orthogonal, Parseval's, Quantum, R2, R3, Reflections, Rn, Rotations
related to Properties · 8
Unitary operator → Borel-measurable, By, L2, Now UU, That, The, This, Use Polarization
related to Definition · 5
Unitary operator → Definition, Hilbert, The, Thus, UU
is a · 4
Unitary operator → bounded linear operator that is both an isometry and a coisometry, bounded linear operator U, generalization of the notion of a unitary matrix, surjective bounded operator on a Hilbert space that preserves the inner product
related to Linearity · 2
Unitary operator → Analogously, The

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Important terminology

unitary operator hilbert space operators bounded product linear inner spaces definition isbn surjective identity isometry matrices rotations uu equivalent following

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Unitary operatoris asurjective bounded operator on a Hilbert space that preserves the inner product0.90text
Unitary operatoris abounded linear operator U0.90text
Unitary operatoris abounded linear operator that is both an isometry and a coisometry0.90text
Unitary operatoris ageneralization of the notion of a unitary matrix0.90text
Unitary operatorrelated to DefinitionDefinition0.60section
Unitary operatorrelated to DefinitionHilbert0.60section
Unitary operatorrelated to DefinitionUU0.60section
Unitary operatorrelated to DefinitionThe0.60section
Unitary operatorrelated to DefinitionThus0.60section
Unitary operatorrelated to ExamplesThe0.60section
Unitary operatorrelated to ExamplesRotations0.60section
Unitary operatorrelated to ExamplesR20.60section

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