"antisymmetric" meaning in All languages combined

See antisymmetric on Wiktionary

Adjective [English]

Etymology: anti- + symmetric. Etymology templates: {{prefix|en|anti|symmetric}} anti- + symmetric Head templates: {{en-adj|-}} antisymmetric (not comparable)
  1. (set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y. Tags: not-comparable Categories (topical): Set theory Translations ((order theory; of a binary relation on a set)): antisymetrický (Czech), malsimetria (Esperanto), antisimetria (Esperanto), antisymmetrinen (Finnish), antisymétrique (French), antisymmetrisch (German), andsamhverfur [masculine] (Icelandic), 反対称的 (han-taishō-teki) (alt: はんたいしょうてき) (Japanese), antysymetryczny (Polish), antissimétrico (Portuguese), antisimetric (Romanian), антисимметри́чный (antisimmetríčnyj) (Russian), antisimétrico (Spanish), antisymmetrisk (Swedish)
    Sense id: en-antisymmetric-en-adj-D-8NsEsh Categories (other): English entries with incorrect language header, English terms prefixed with anti- Disambiguation of English entries with incorrect language header: 29 11 30 30 Disambiguation of English terms prefixed with anti-: 27 23 23 27 Topics: mathematics, order-theory, sciences, set-theory Disambiguation of '(order theory; of a binary relation on a set)': 59 12 12 16
  2. (linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof:
    (of a matrix) Whose transpose equals its negative (i.e., Mᵀ = −M);
    Tags: not-comparable Categories (topical): Linear algebra
    Sense id: en-antisymmetric-en-adj-UEtG5EB5 Categories (other): English entries with incorrect language header, English terms prefixed with anti- Disambiguation of English entries with incorrect language header: 29 11 30 30 Disambiguation of English terms prefixed with anti-: 27 23 23 27 Topics: linear-algebra, mathematics, sciences
  3. (linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof:
    (of a tensor) That changes sign when any two indices are interchanged (e.g., Tᵢⱼₖ = -Tⱼᵢₖ);
    Tags: not-comparable Categories (topical): Linear algebra
    Sense id: en-antisymmetric-en-adj-Egwo4D6G Categories (other): English entries with incorrect language header, English terms prefixed with anti- Disambiguation of English entries with incorrect language header: 29 11 30 30 Disambiguation of English terms prefixed with anti-: 27 23 23 27 Topics: linear-algebra, mathematics, sciences
  4. (linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof:
    (of a bilinear form) For which B(w,v) = -B(v,w).
    Tags: not-comparable Categories (topical): Linear algebra
    Sense id: en-antisymmetric-en-adj-cJoedBOE Categories (other): English entries with incorrect language header, English terms prefixed with anti- Disambiguation of English entries with incorrect language header: 29 11 30 30 Disambiguation of English terms prefixed with anti-: 27 23 23 27 Topics: linear-algebra, mathematics, sciences
The following are not (yet) sense-disambiguated
Synonyms: skew-symmetric [linear-algebra, mathematics, sciences] Derived forms: antisymmetrically, antisymmetricity Related terms: antisymmetry, symmetric, anticommutative, skew-symmetric Translations ((linear algebra)): antisymmetrinen (Finnish), antisymmetrisch (German), antysymetryczny (Polish), antisimetric (Romanian), antisimétrico (Spanish)
Disambiguation of '(linear algebra)': 10 28 28 34

Download JSON data for antisymmetric meaning in All languages combined (10.5kB)

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  "etymology_text": "anti- + symmetric.",
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          "ref": "2006, S. C. Sharma, Metric Space, Discovery Publishing House, page 73",
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          "_dis1": "59 12 12 16",
          "code": "fr",
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          "word": "antisimetric"
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          "word": "антисимметри́чный"
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          "_dis1": "59 12 12 16",
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          "ref": "2012, Stephanie Frank Singer, Symmetry in Mechanics: A Gentle, Modern Introduction, Springer, page 28",
          "text": "Antisymmetric bilinear forms and wedge products are defined exactly as above, only now they are functions from #x5C;Rⁿ#x5C;times#x5C;Rⁿ to #x5C;R.[…]\nExercise 21 Show that every antisymmetric bilinear form on #x5C;R³ is a wedge product of two covectors.",
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      "word": "skew-symmetric"
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  "translations": [
    {
      "_dis1": "10 28 28 34",
      "code": "fi",
      "lang": "Finnish",
      "sense": "(linear algebra)",
      "word": "antisymmetrinen"
    },
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      "sense": "(linear algebra)",
      "word": "antisymmetrisch"
    },
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      "sense": "(linear algebra)",
      "word": "antisimetric"
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      "word": "antisimétrico"
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  "word": "antisymmetric"
}
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        },
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      ],
      "raw_glosses": [
        "(linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof:",
        "(of a tensor) That changes sign when any two indices are interchanged (e.g., Tᵢⱼₖ = -Tⱼᵢₖ);"
      ],
      "raw_tags": [
        "of a tensor",
        "of certain mathematical objects"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "en:Linear algebra"
      ],
      "examples": [
        {
          "ref": "2012, Stephanie Frank Singer, Symmetry in Mechanics: A Gentle, Modern Introduction, Springer, page 28",
          "text": "Antisymmetric bilinear forms and wedge products are defined exactly as above, only now they are functions from #x5C;Rⁿ#x5C;times#x5C;Rⁿ to #x5C;R.[…]\nExercise 21 Show that every antisymmetric bilinear form on #x5C;R³ is a wedge product of two covectors.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Whose sign changes on the application of a matrix transpose or some generalisation thereof:",
        "For which B(w,v) = -B(v,w)."
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "transpose",
          "transpose"
        ],
        [
          "bilinear form",
          "bilinear form"
        ]
      ],
      "raw_glosses": [
        "(linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof:",
        "(of a bilinear form) For which B(w,v) = -B(v,w)."
      ],
      "raw_tags": [
        "of a bilinear form",
        "of certain mathematical objects"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "word": "skew-symmetric"
    }
  ],
  "translations": [
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisymetrický"
    },
    {
      "code": "eo",
      "lang": "Esperanto",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "malsimetria"
    },
    {
      "code": "eo",
      "lang": "Esperanto",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisimetria"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisymmetrinen"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisymétrique"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisymmetrisch"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "(order theory; of a binary relation on a set)",
      "tags": [
        "masculine"
      ],
      "word": "andsamhverfur"
    },
    {
      "alt": "はんたいしょうてき",
      "code": "ja",
      "lang": "Japanese",
      "roman": "han-taishō-teki",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "反対称的"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antysymetryczny"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antissimétrico"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisimetric"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "antisimmetríčnyj",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "антисимметри́чный"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisimétrico"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "(order theory; of a binary relation on a set)",
      "word": "antisymmetrisk"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "(linear algebra)",
      "word": "antisymmetrinen"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "(linear algebra)",
      "word": "antisymmetrisch"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "(linear algebra)",
      "word": "antysymetryczny"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "(linear algebra)",
      "word": "antisimetric"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "(linear algebra)",
      "word": "antisimétrico"
    }
  ],
  "wikipedia": [
    "antisymmetric"
  ],
  "word": "antisymmetric"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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.