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- Levi-Civita_symbol abstract "In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers 1, 2, …, n, for some positive integer n. It is named after the Italian mathematician and physicist Tullio Levi-Civita. Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations.The standard letters to denote the Levi-Civita symbol are the Greek lower case epsilon ε or ϵ, or less commonly the Latin lower case e. Index notation allows one to display permutations in a way compatible with tensor analysis:where each index i1, i2, …, in takes values 1, 2, …, n. There are nn indexed values of , which can be arranged into an n-dimensional array. The key definitive property of the symbol is total antisymmetry in all the indices. When any two indices are interchanged, equal or not, the symbol is negated:If any two indices are equal, the symbol is zero. When all indices are unequal, we have:where p (called the parity of the permutation) is the number of interchanges of indices necessary to unscramble i1, i2, …, in into the order 1, 2, …, n, and the factor (−1)p is called the sign or signature of the permutation. The value ε12…n must be defined, else the particular values of the symbol for all permutations are indeterminate. Most authors choose ε12…n = +1, which means the Levi-Civita symbol equals the sign of a permutation when the indices are all unequal. This choice is used throughout this article.The term "n-dimensional Levi-Civita symbol" refers to the fact that the number of indices on the symbol n matches the dimensionality of the relevant vector space in question, which may be Euclidean or non-Euclidean, pure space or spacetime. The values of the Levi-Civita symbol are independent of any metric tensor and coordinate system.The Levi-Civita symbol may be used to express the determinant of a square matrix and the cross product of two vectors in 3d Euclidean space.".
- Levi-Civita_symbol wikiPageExternalLink PermutationTensor.html.
- Levi-Civita_symbol wikiPageID "195982".
- Levi-Civita_symbol wikiPageRevisionID "605747829".
- Levi-Civita_symbol b "β…".
- Levi-Civita_symbol hasPhotoCollection Levi-Civita_symbol.
- Levi-Civita_symbol id "4116".
- Levi-Civita_symbol p "α…".
- Levi-Civita_symbol title "Levi-Civita permutation symbol".
- Levi-Civita_symbol subject Category:Articles_containing_proofs.
- Levi-Civita_symbol subject Category:Linear_algebra.
- Levi-Civita_symbol subject Category:Permutations.
- Levi-Civita_symbol subject Category:Tensors.
- Levi-Civita_symbol type Abstraction100002137.
- Levi-Civita_symbol type Change107296428.
- Levi-Civita_symbol type Cognition100023271.
- Levi-Civita_symbol type Concept105835747.
- Levi-Civita_symbol type Content105809192.
- Levi-Civita_symbol type Event100029378.
- Levi-Civita_symbol type Happening107283608.
- Levi-Civita_symbol type Idea105833840.
- Levi-Civita_symbol type Permutations.
- Levi-Civita_symbol type PsychologicalFeature100023100.
- Levi-Civita_symbol type Quantity105855125.
- Levi-Civita_symbol type Substitution107443761.
- Levi-Civita_symbol type Tensor105864481.
- Levi-Civita_symbol type Tensors.
- Levi-Civita_symbol type Variable105857459.
- Levi-Civita_symbol type Variation107337390.
- Levi-Civita_symbol type YagoPermanentlyLocatedEntity.
- Levi-Civita_symbol comment "In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers 1, 2, …, n, for some positive integer n. It is named after the Italian mathematician and physicist Tullio Levi-Civita.".
- Levi-Civita_symbol label "Levi-Civita symbol".
- Levi-Civita_symbol label "Levi-Civita-Symbol".
- Levi-Civita_symbol label "Simbolo di Levi-Civita".
- Levi-Civita_symbol label "Symbol Leviego-Civity".
- Levi-Civita_symbol label "Symbole de Levi-Civita".
- Levi-Civita_symbol label "Símbolo de Levi-Civita".
- Levi-Civita_symbol label "Símbolo de Levi-Civita".
- Levi-Civita_symbol label "Символ Леви-Чивиты".
- Levi-Civita_symbol label "エディントンのイプシロン".
- Levi-Civita_symbol label "列維-奇維塔符號".
- Levi-Civita_symbol sameAs Levi-Civitův_symbol.
- Levi-Civita_symbol sameAs Levi-Civita-Symbol.
- Levi-Civita_symbol sameAs Σύμβολο_μετάθεσης.
- Levi-Civita_symbol sameAs Símbolo_de_Levi-Civita.
- Levi-Civita_symbol sameAs Symbole_de_Levi-Civita.
- Levi-Civita_symbol sameAs Simbolo_di_Levi-Civita.
- Levi-Civita_symbol sameAs エディントンのイプシロン.
- Levi-Civita_symbol sameAs 레비치비타_기호.
- Levi-Civita_symbol sameAs Levi-civita-symbool.
- Levi-Civita_symbol sameAs Symbol_Leviego-Civity.
- Levi-Civita_symbol sameAs Símbolo_de_Levi-Civita.
- Levi-Civita_symbol sameAs m.01bvm8.
- Levi-Civita_symbol sameAs Q623761.
- Levi-Civita_symbol sameAs Q623761.
- Levi-Civita_symbol sameAs Levi-Civita_symbol.
- Levi-Civita_symbol wasDerivedFrom Levi-Civita_symbol?oldid=605747829.
- Levi-Civita_symbol isPrimaryTopicOf Levi-Civita_symbol.