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Hodge star operator

In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge.

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Duality

On manifolds

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Hodge star operator

Nodes100
Edges99
Triples22
Avg. degree1.98
Density0.02
Components1

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Hodge star operator

Top relations

related to Four dimensions · 10
Hodge star operator → Duality, For, Hodge, If, In, Minkowski, Riemannian, That, The, This
related to Three dimensions · 5
Hodge star operator → Applied, Euclidean R3, Hodge, Specifically, The Hodge
is a · 2
Hodge star operator → case n, linear operator on the exterior algebra of V

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Important terminology

displaystyle star hodge operator wedge space dx vector form dual exterior delta right product basis textstyle left codifferential dy oriented

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hodge star operatoris alinear operator on the exterior algebra of V0.90text
Hodge star operatoris acase n0.90text
pseudo-Riemannian manifoldsinstance ofIn more general contexts0.80text
Minkowski spaceinstance ofIn more general contexts0.80text
the bilinear form may not be positive-definiteinstance ofIn more general contexts0.80text
spinor-helicity formalism or twistor theory.Conformal invarianceThe Hodge star is conformally invariant on n-forms on a 2n-dimensional vector space Vinstance ofmaking contacts to the use of the two-spinor language in modern physics0.80text
spinor-helicity formalism or twistor theoryinstance ofmaking contacts to the use of the two-spinor language in modern physics0.80text
Hodge star operatorrelated to Four dimensionsIn0.60section
Hodge star operatorrelated to Four dimensionsHodge0.60section
Hodge star operatorrelated to Four dimensionsIf0.60section
Hodge star operatorrelated to Four dimensionsRiemannian0.60section
Hodge star operatorrelated to Four dimensionsDuality0.60section

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