See Kronecker delta in All languages combined, or Wiktionary
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Deissler, Turbulent Fluid Motion, Taylor & Francis, page 24:", "text": "The Kronecker delta #92;delta#95;#123;ij#125; is an example of an isotropic tensor. That is, its components remain invariant with rotation of coordinate axes.", "type": "quote" }, { "ref": "2007, J. N. Reddy, An Introduction to Continuum Mechanics, Cambridge University Press, page 20, Further, the Kronecker delta and the permutation symbol are related by the identity, known as the e-δ identity [see Problem 2.5(d)], e_ijke_imn=δⱼₘδₖₙ-δⱼₙδₖₘ. (2.2.43)", "text": "The permutation symbol and the Kronecker delta prove to be very useful in proving vector identities." }, { "ref": "2017, Sadri Hassani, Special Relativity: A Heuristic Approach, Elsevier, page 257:", "text": "The most important property of the Kronecker delta occurs when it shares a common repeated index with another tensor:\nNote 10.1.3. When an index of a tensor T is contracted with one of the indices of the Kronecker delta, the result is an expression in which the Kronecker delta is removed and the contracted index of T is replaced by the other index of the Kronecker delta.", "type": "quote" } ], "glosses": [ "A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise." ], "id": "en-Kronecker_delta-en-noun-m5rxBhJm", "links": [ [ "mathematics", "mathematics" ], [ "binary", "binary" ], [ "function", "function" ], [ "subscript", "subscript" ], [ "evaluate", "evaluate" ], [ "argument", "argument" ] ], "raw_glosses": [ "(mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise." ], "related": [ { "_dis1": "86 14", "word": "Dirac delta" }, { "_dis1": "86 14", "word": "Dirac delta function" }, { "_dis1": "86 14", "word": "Dirac measure" }, { "_dis1": "86 14", "word": "Iverson bracket" }, { "_dis1": "86 14", "word": "Kronecker product" }, { "_dis1": "86 14", "word": "Kronecker symbol" }, { "_dis1": "86 14", "word": "Levi-Civita symbol" } ], "synonyms": [ { "_dis1": "88 12", "sense": "binary function", "word": "Kronecker tensor" }, { "_dis1": "88 12", "sense": "binary function", "word": "substitution tensor" } ], "topics": [ "mathematics", "sciences" ], "translations": [ { "_dis1": "89 11", "code": "cmn", "lang": "Chinese Mandarin", "roman": "Kèluónèikè'ěr δ", "sense": "Translations", "word": "克羅內克爾δ /克罗内克尔δ" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere." ], "id": "en-Kronecker_delta-en-noun-nZRG1x0H", "links": [ [ "mathematics", "mathematics" ], [ "unary", "unary" ], [ "function", "function" ], [ "index", "index" ], [ "evaluate", "evaluate" ] ], "raw_glosses": [ "(mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere." ], "topics": [ "mathematics", "sciences" ] } ], "wikipedia": [ "Kronecker delta" ], "word": "Kronecker delta" }
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