See multilinear form in All languages combined, or Wiktionary
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C. Power (editor) Operators and Function Theory, Kluwer Academic (D. Reidel), page 163,\nFinally, in the short Lecture 5 we make some remarks on multilinear forms over Hilbert spaces, a theory which is still in a rather embryonic state, motivated by the observation that paracommutators (and Hankel operators too) really should be viewed as forms, not operators." }, { "text": "1994, Hessam Khoshnevisan, Mohamad Afshar, Mechanical Elimination of Commutative Redundancy, Baudouin Le Charlier (editor), Static Analysis: 1st International Static Analysis Symposium, Proceedings, Volume 1, Springer, LNCS 864, page 454,\nA multilinear form is said to be degenerate if all its function variables are identical. Thus a degenerate m-multilinear form can more concisely be written as M!f." }, { "ref": "2003, Maks A. Akivis, Vladislav V. Goldberg, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 55:", "text": "Since the coordinates of a vector change in transforming to a new basis, the same is true of the coefficients of a multilinear form (since the form itself is to remain invariant).", "type": "quote" } ], "glosses": [ "Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;" ], "id": "en-multilinear_form-en-noun-5~KZ36rg", "links": [ [ "linear algebra", "linear algebra" ], [ "vector space", "vector space" ], [ "scalar", "scalar" ], [ "mapping", "mapping" ], [ "linear", "linear" ], [ "module", "module" ], [ "commutative ring", "commutative ring" ] ], "qualifier": "multilinear algebra", "raw_glosses": [ "(linear algebra, multilinear algebra) Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;" ], "topics": [ "linear-algebra", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Linear algebra", "orig": "en:Linear algebra", "parents": [ "Algebra", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "44 56", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "26 74", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "43 57", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "36 64", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "30 70", "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w+disamb" }, { "_dis": "30 70", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "26 74", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;\n(more generally) a similarly multiply linear mapping Mʳ → R defined for a given module M over some commutative ring R.", "a similarly multiply linear mapping Mʳ → R defined for a given module M over some commutative ring R." ], "id": "en-multilinear_form-en-noun-ZlCNN~C4", "links": [ [ "linear algebra", "linear algebra" ], [ "vector space", "vector space" ], [ "scalar", "scalar" ], [ "mapping", "mapping" ], [ "linear", "linear" ], [ "module", "module" ], [ "commutative ring", "commutative ring" ] ], "qualifier": "multilinear algebra", "raw_glosses": [ "(linear algebra, multilinear algebra) Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;" ], "tags": [ "broadly" ], "topics": [ "linear-algebra", "mathematics", "sciences" ] } ], "synonyms": [ { "_dis1": "45 55", "sense": "multiply linear mapping to a field of scalars", "word": "multicovector" } ], "translations": [ { "_dis1": "45 55", "code": "fr", "lang": "French", "sense": "multiply linear mapping to a field of scalars", "tags": [ "feminine" ], "word": "forme multilinéaire" }, { "_dis1": "45 55", "code": "de", "lang": "German", "sense": "multiply linear mapping to a field of scalars", "tags": [ "feminine" ], "word": "Multilinearform" }, { "_dis1": "45 55", "code": "es", "lang": "Spanish", "sense": "multiply linear mapping to a field of scalars", "tags": [ "feminine" ], "word": "forma multilineal" }, { "_dis1": "45 55", "code": "es", "lang": "Spanish", "sense": "multiply linear mapping to a field of scalars", "tags": [ "feminine" ], "word": "función multilineal" } ], "wikipedia": [ "multilinear form" ], "word": "multilinear form" }
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