"multilinear form" meaning in English

See multilinear form in All languages combined, or Wiktionary

Noun

Forms: multilinear forms [plural]
Head templates: {{en-noun}} multilinear form (plural multilinear forms)
  1. (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; Categories (topical): Linear algebra
    Sense id: en-multilinear_form-en-noun-5~KZ36rg Topics: linear-algebra, mathematics, sciences
  2. (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 Categories (topical): Linear algebra
    Sense id: en-multilinear_form-en-noun-ZlCNN~C4 Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with French translations, Terms with German translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 44 56 Disambiguation of Entries with translation boxes: 26 74 Disambiguation of Pages with 1 entry: 42 58 Disambiguation of Pages with entries: 36 64 Disambiguation of Terms with French translations: 30 70 Disambiguation of Terms with German translations: 30 70 Disambiguation of Terms with Spanish translations: 26 74 Topics: linear-algebra, mathematics, sciences
The following are not (yet) sense-disambiguated
Synonyms (multiply linear mapping to a field of scalars): multicovector Hyponyms (multiply linear mapping to a field of scalars): bilinear form, covector, linear form Derived forms: alternating multilinear form, multilinear k-form Related terms: covariant, differential form, linear, linear form, multilinear algebra, multilinear map, multivector, tensor Translations (multiply linear mapping to a field of scalars): forme multilinéaire [feminine] (French), Multilinearform [feminine] (German), forma multilineal [feminine] (Spanish), función multilineal [feminine] (Spanish)
Disambiguation of 'multiply linear mapping to a field of scalars': 45 55 Disambiguation of 'multiply linear mapping to a field of scalars': 45 55 Disambiguation of 'multiply linear mapping to a field of scalars': 45 55

Inflected forms

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      "word": "alternating multilinear form"
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      "_dis1": "52 48",
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      "_dis1": "45 55",
      "sense": "multiply linear mapping to a field of scalars",
      "word": "covector"
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      "_dis1": "52 48",
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      "_dis1": "52 48",
      "word": "differential form"
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      "_dis1": "52 48",
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      "_dis1": "52 48",
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          "text": "1985, Jack Peetre, Paracommutators and Minimal Spaces, S. 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"
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        "(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;"
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        "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."
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      "_dis1": "45 55",
      "sense": "multiply linear mapping to a field of scalars",
      "word": "multicovector"
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      "code": "fr",
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      "sense": "multiply linear mapping to a field of scalars",
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      "sense": "multiply linear mapping to a field of scalars",
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    },
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      "sense": "multiply linear mapping to a field of scalars",
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    }
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  "word": "multilinear form"
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        },
        {
          "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."
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      "sense": "multiply linear mapping to a field of scalars",
      "word": "multicovector"
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      "code": "fr",
      "lang": "French",
      "sense": "multiply linear mapping to a field of scalars",
      "tags": [
        "feminine"
      ],
      "word": "forme multilinéaire"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "multiply linear mapping to a field of scalars",
      "tags": [
        "feminine"
      ],
      "word": "Multilinearform"
    },
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      "tags": [
        "feminine"
      ],
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    },
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      "tags": [
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    }
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  "word": "multilinear form"
}

Download raw JSONL data for multilinear form meaning in English (4.6kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-10-22 from the enwiktionary dump dated 2024-10-02 using wiktextract (eaa6b66 and a709d4b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.