"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: 43 57 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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      "_dis1": "52 48",
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      "_dis1": "45 55",
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      "word": "covector"
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      "_dis1": "52 48",
      "word": "covariant"
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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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        "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",
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      "word": "multicovector"
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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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      "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 2024-12-08 from the enwiktionary dump dated 2024-12-04 using wiktextract (bb46d54 and 0c3c9f6). 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.

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