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Min-max theorem

In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces. It can be viewed as the starting point of many results of similar nature.

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Applications

Singular valuesCompressionOrthogonal projectionMajorization
4 related topics

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ArXivDoiJSTORISBN
4 related topics

Matrices

Hermitian matrixRayleigh–Ritz quotientEuclidean inner productPartial trace
4 related topics

Compact operators

HermitianSpectrumCluster pointMultiplicity
4 related topics

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Matrices

Applications

Compact operators

Self-adjoint operators

External links and citations to related work

  • ArXiv ArXiv (identifier)
  • Doi Doi (identifier)
  • JSTOR JSTOR (identifier)
  • ISBN ISBN (identifier)

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Min-max theorem

Nodes31
Edges30
Triples8
Avg. degree1.94
Density0.064516
Components1

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Min-max theorem

Top relations

related to Min-max principle for singular values · 4
Min-max theorem → An, MM, Similarly, The
related to Self-adjoint operators · 3
Min-max theorem → Recall, Sometimes, The
is a · 1
Min-max theorem → refinement of this fact.Min-max theoremLet A

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Important terminology

textstyle displaystyle theorem lambda operators compact min-max eigenvalues hermitian geq span case leq subset dots tr cdots inequality spectrum matrix

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Min-max theoremis arefinement of this fact.Min-max theoremLet A0.90text
Min-max theoremrelated to Min-max principle for singular valuesThe0.60section
Min-max theoremrelated to Min-max principle for singular valuesMM0.60section
Min-max theoremrelated to Min-max principle for singular valuesAn0.60section
Min-max theoremrelated to Min-max principle for singular valuesSimilarly0.60section
Min-max theoremrelated to Self-adjoint operatorsThe0.60section
Min-max theoremrelated to Self-adjoint operatorsRecall0.60section
Min-max theoremrelated to Self-adjoint operatorsSometimes0.60section

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    Min side: 3
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