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Trace class

In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent of the choice of basis used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra. All trace-class operators are…

Properties, Definition & Equivalent formulations

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Map overview Semantic statistics

Trace class

Nodes68
Edges67
Triples38
Avg. degree1.97
Density0.029412
Components1

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Trace class

Top relations

related to Properties · 15
Trace class → Ae, AT, Be, Ce, Fredholm, Furthermore, Hilbert, Hilbert-Schmidt, If, It, Schmidt, TA, The, Therefore, Tr
related to Equivalent formulations · 6
Trace class → CT, Given, Hilbert-Schmidt, If, There, Tr
related to Finite-rank operators · 6
Trace class → Ax, Every, Furthermore, Given, Then, Tr
related to Definition · 4
Trace class → Hilbert, Let, The, Tr
related to Mercer's theorem · 4
Trace class → Hilbert, Mercer's, Schmidt, That
related to Spectral theorem · 3
Trace class → Hilbert, Let, Then

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Important terminology

displaystyle operator trace operators trace-class tr class right left operatorname hilbert space langle rangle linear positive bounded compact sum leq

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Trace classrelated to DefinitionLet0.60section
Trace classrelated to DefinitionHilbert0.60section
Trace classrelated to DefinitionThe0.60section
Trace classrelated to DefinitionTr0.60section
Trace classrelated to Equivalent formulationsGiven0.60section
Trace classrelated to Equivalent formulationsTr0.60section
Trace classrelated to Equivalent formulationsThere0.60section
Trace classrelated to Equivalent formulationsIf0.60section
Trace classrelated to Equivalent formulationsCT0.60section
Trace classrelated to Equivalent formulationsHilbert-Schmidt0.60section
Trace classrelated to Finite-rank operatorsEvery0.60section
Trace classrelated to Finite-rank operatorsFurthermore0.60section

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