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Singular value

In mathematics, in particular in functional analysis, the singular values of a compact operator T : X → Y {\displaystyle \,T\!:X\rightarrow Y} acting between Hilbert spaces X {\displaystyle X} and ⁠ Y {\displaystyle Y} ⁠, are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T ∗ T {\displaystyle T^{*}T} (where T…

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Overview

MathematicsFunctional analysisCompact operatorHilbert spacesEigenvalues
23 related topics

History

Erhard SchmidtBanach spacesS-numbers
3 related topics

Basic properties

TraceAugmented
2 related topics

Inequalities about singular values

Weyl's theorem
1 related topics

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Overview

Basic properties

Inequalities about singular values

History

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Singular value

Nodes34
Edges33
Triples16
Avg. degree1.94
Density0.058824
Components1

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Singular value

Top relations

related to history · 8
Singular value → Allahverdiev, Banach, Erhard Schmidt, In, Schmidt, Smithies, The, This
related to Basic properties · 3
Singular value → For, Here, Min-max
see also · 3
Singular value → Condition, Horn, Poincaré
related to The smallest singular value · 2
Singular value → For, The

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Important terminology

displaystyle singular sigma values leq eigenvalues value left right matrix times mathbb theorem lambda sum norm see min ldots mathrm

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Singular valuerelated to Basic propertiesFor0.60section
Singular valuerelated to Basic propertiesMin-max0.60section
Singular valuerelated to Basic propertiesHere0.60section
Singular valuerelated to historyThis0.60section
Singular valuerelated to historyErhard Schmidt0.60section
Singular valuerelated to historySchmidt0.60section
Singular valuerelated to historyThe0.60section
Singular valuerelated to historySmithies0.60section
Singular valuerelated to historyIn0.60section
Singular valuerelated to historyAllahverdiev0.60section
Singular valuerelated to historyBanach0.60section
Singular valuerelated to The smallest singular valueThe0.60section

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    Min side: 3
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