"vector space" meaning in English

See vector space in All languages combined, or Wiktionary

Noun

Forms: vector spaces [plural]
Head templates: {{en-noun}} vector space (plural vector spaces)
  1. (algebra, geometry, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints. Wikipedia link: vector space Categories (topical): Algebra, Geometry, Linear algebra, Mathematical analysis, Topology Synonyms: linear space Hypernyms: module, free module Hyponyms: algebra over a field, Banach space, Euclidean space, inner product space, normed vector space, quadratic space, real vector space Meronyms: linear subspace, subspace, vector Translations (mathematics): vektorruimte (Afrikaans), վեկտորական տարածություն (vektorakan taracutʿyun) (Armenian), espaciu vectorial [masculine] (Asturian), bektore espazio (Basque), вектарная прастора (vjektarnaja prastóra) [feminine] (Belarusian), espai vectorial [masculine] (Catalan), 向量空間 (Chinese Mandarin), 向量空间 (xiàngliàng kōngjiān) (Chinese Mandarin), 矢量空間 (Chinese Mandarin), 矢量空间 (shǐliàng kōngjiān) (Chinese Mandarin), vektorový prostor [masculine] (Czech), vektorrum [neuter] (Danish), vectorruimte [feminine] (Dutch), vektora spaco (Esperanto), vektorruum (Estonian), vektoriavaruus (Finnish), espace vectoriel [masculine] (French), espazo vectorial [masculine] (Galician), Vektorraum [masculine] (German), διανυσματικός χώρος (dianysmatikós chóros) [masculine] (Greek), vektortér (Hungarian), vigurrúm [neuter] (Icelandic), ruang vektor (Indonesian), spatio vectorial (Interlingua), spás veicteoireach [masculine] (Irish), spazio vettoriale [masculine] (Italian), ベクトル空間 (bekutoru kūkan) (Japanese), 벡터 공간 (bekteo gonggan) (Korean), вектордук мейкиндик (vektorduk meykindik) (Kyrgyz), vektorinė erdvė [feminine] (Lithuanian), векторски простор (vektorski prostor) [masculine] (Macedonian), ruang vektor (Malay), സദിശസമഷ്ടി (sadiśasamaṣṭi) (Malayalam), vektorrom [neuter] (Norwegian), فضای برداری (Persian), przestrzeń wektorowa [feminine] (Polish), przestrzeń liniowa [feminine] (Polish), espaço vetorial [masculine] (Portuguese), spațiu vectorial [neuter] (Romanian), ве́кторное простра́нство (véktornoje prostránstvo) [neuter] (Russian), vektorski prostor [masculine] (Serbo-Croatian), vektorový priestor [masculine] (Slovak), vektorski prostor [masculine] (Slovene), espacio vectorial [masculine] (Spanish), vektorrum [neuter] (Swedish), espasyong bektor (Tagalog), திசையன் வெளி (ticaiyaṉ veḷi) (Tamil), ปริภูมิเวกเตอร์ (Thai), ปริภูมิเชิงเส้น (Thai), vektör uzayı (Turkish), векторний простір (vektornyj prostir) [masculine] (Ukrainian), không gian vectơ (Vietnamese)

Inflected forms

Download JSON data for vector space meaning in English (9.1kB)

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          "text": "A vector space is a set of vectors which can be linearly combined."
        },
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          "text": "Each vector space has a basis and dimension."
        }
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        "A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints."
      ],
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        {
          "word": "module"
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          "word": "free module"
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          "word": "algebra over a field"
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          "word": "Banach space"
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          "word": "Euclidean space"
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          "word": "inner product space"
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          "word": "normed vector space"
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          "word": "quadratic space"
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          "set",
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          "vector",
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          "field",
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          "addition",
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          "word": "subspace"
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      "translations": [
        {
          "code": "af",
          "lang": "Afrikaans",
          "sense": "mathematics",
          "word": "vektorruimte"
        },
        {
          "code": "hy",
          "lang": "Armenian",
          "roman": "vektorakan taracutʿyun",
          "sense": "mathematics",
          "word": "վեկտորական տարածություն"
        },
        {
          "code": "ast",
          "lang": "Asturian",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "espaciu vectorial"
        },
        {
          "code": "eu",
          "lang": "Basque",
          "sense": "mathematics",
          "word": "bektore espazio"
        },
        {
          "code": "be",
          "lang": "Belarusian",
          "roman": "vjektarnaja prastóra",
          "sense": "mathematics",
          "tags": [
            "feminine"
          ],
          "word": "вектарная прастора"
        },
        {
          "code": "ca",
          "lang": "Catalan",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "espai vectorial"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "sense": "mathematics",
          "word": "向量空間"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "xiàngliàng kōngjiān",
          "sense": "mathematics",
          "word": "向量空间"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "sense": "mathematics",
          "word": "矢量空間"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "shǐliàng kōngjiān",
          "sense": "mathematics",
          "word": "矢量空间"
        },
        {
          "code": "cs",
          "lang": "Czech",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "vektorový prostor"
        },
        {
          "code": "da",
          "lang": "Danish",
          "sense": "mathematics",
          "tags": [
            "neuter"
          ],
          "word": "vektorrum"
        },
        {
          "code": "nl",
          "lang": "Dutch",
          "sense": "mathematics",
          "tags": [
            "feminine"
          ],
          "word": "vectorruimte"
        },
        {
          "code": "eo",
          "lang": "Esperanto",
          "sense": "mathematics",
          "word": "vektora spaco"
        },
        {
          "code": "et",
          "lang": "Estonian",
          "sense": "mathematics",
          "word": "vektorruum"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "mathematics",
          "word": "vektoriavaruus"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "espace vectoriel"
        },
        {
          "code": "gl",
          "lang": "Galician",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "espazo vectorial"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "Vektorraum"
        },
        {
          "code": "el",
          "lang": "Greek",
          "roman": "dianysmatikós chóros",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "διανυσματικός χώρος"
        },
        {
          "code": "hu",
          "lang": "Hungarian",
          "sense": "mathematics",
          "word": "vektortér"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "mathematics",
          "tags": [
            "neuter"
          ],
          "word": "vigurrúm"
        },
        {
          "code": "id",
          "lang": "Indonesian",
          "sense": "mathematics",
          "word": "ruang vektor"
        },
        {
          "code": "ia",
          "lang": "Interlingua",
          "sense": "mathematics",
          "word": "spatio vectorial"
        },
        {
          "code": "ga",
          "lang": "Irish",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "spás veicteoireach"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "spazio vettoriale"
        },
        {
          "code": "ja",
          "lang": "Japanese",
          "roman": "bekutoru kūkan",
          "sense": "mathematics",
          "word": "ベクトル空間"
        },
        {
          "code": "ko",
          "lang": "Korean",
          "roman": "bekteo gonggan",
          "sense": "mathematics",
          "word": "벡터 공간"
        },
        {
          "code": "ky",
          "lang": "Kyrgyz",
          "roman": "vektorduk meykindik",
          "sense": "mathematics",
          "word": "вектордук мейкиндик"
        },
        {
          "code": "lt",
          "lang": "Lithuanian",
          "sense": "mathematics",
          "tags": [
            "feminine"
          ],
          "word": "vektorinė erdvė"
        },
        {
          "code": "mk",
          "lang": "Macedonian",
          "roman": "vektorski prostor",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "векторски простор"
        },
        {
          "code": "ms",
          "lang": "Malay",
          "sense": "mathematics",
          "word": "ruang vektor"
        },
        {
          "code": "ml",
          "lang": "Malayalam",
          "roman": "sadiśasamaṣṭi",
          "sense": "mathematics",
          "word": "സദിശസമഷ്ടി"
        },
        {
          "code": "no",
          "lang": "Norwegian",
          "sense": "mathematics",
          "tags": [
            "neuter"
          ],
          "word": "vektorrom"
        },
        {
          "code": "fa",
          "lang": "Persian",
          "sense": "mathematics",
          "word": "فضای برداری"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "mathematics",
          "tags": [
            "feminine"
          ],
          "word": "przestrzeń wektorowa"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "mathematics",
          "tags": [
            "feminine"
          ],
          "word": "przestrzeń liniowa"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "espaço vetorial"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "mathematics",
          "tags": [
            "neuter"
          ],
          "word": "spațiu vectorial"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "véktornoje prostránstvo",
          "sense": "mathematics",
          "tags": [
            "neuter"
          ],
          "word": "ве́кторное простра́нство"
        },
        {
          "code": "sh",
          "lang": "Serbo-Croatian",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "vektorski prostor"
        },
        {
          "code": "sk",
          "lang": "Slovak",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "vektorový priestor"
        },
        {
          "code": "sl",
          "lang": "Slovene",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "vektorski prostor"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "espacio vectorial"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "mathematics",
          "tags": [
            "neuter"
          ],
          "word": "vektorrum"
        },
        {
          "code": "tl",
          "lang": "Tagalog",
          "sense": "mathematics",
          "word": "espasyong bektor"
        },
        {
          "code": "ta",
          "lang": "Tamil",
          "roman": "ticaiyaṉ veḷi",
          "sense": "mathematics",
          "word": "திசையன் வெளி"
        },
        {
          "code": "th",
          "lang": "Thai",
          "sense": "mathematics",
          "word": "ปริภูมิเวกเตอร์"
        },
        {
          "code": "th",
          "lang": "Thai",
          "sense": "mathematics",
          "word": "ปริภูมิเชิงเส้น"
        },
        {
          "code": "tr",
          "lang": "Turkish",
          "sense": "mathematics",
          "word": "vektör uzayı"
        },
        {
          "code": "uk",
          "lang": "Ukrainian",
          "roman": "vektornyj prostir",
          "sense": "mathematics",
          "tags": [
            "masculine"
          ],
          "word": "векторний простір"
        },
        {
          "code": "vi",
          "lang": "Vietnamese",
          "sense": "mathematics",
          "word": "không gian vectơ"
        }
      ],
      "wikipedia": [
        "vector space"
      ]
    }
  ],
  "word": "vector space"
}
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      "word": "algebra over a field"
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      "word": "Banach space"
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      "word": "Euclidean space"
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    {
      "word": "inner product space"
    },
    {
      "word": "normed vector space"
    },
    {
      "word": "quadratic space"
    },
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      "word": "real vector space"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "word": "linear subspace"
    },
    {
      "word": "subspace"
    },
    {
      "word": "vector"
    }
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  "pos": "noun",
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      "examples": [
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          "text": "A vector space is a set of vectors which can be linearly combined."
        },
        {
          "text": "Each vector space has a basis and dimension."
        }
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      "glosses": [
        "A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints."
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        "(algebra, geometry, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints."
      ],
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      "wikipedia": [
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  "synonyms": [
    {
      "word": "linear space"
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  ],
  "translations": [
    {
      "code": "af",
      "lang": "Afrikaans",
      "sense": "mathematics",
      "word": "vektorruimte"
    },
    {
      "code": "hy",
      "lang": "Armenian",
      "roman": "vektorakan taracutʿyun",
      "sense": "mathematics",
      "word": "վեկտորական տարածություն"
    },
    {
      "code": "ast",
      "lang": "Asturian",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "espaciu vectorial"
    },
    {
      "code": "eu",
      "lang": "Basque",
      "sense": "mathematics",
      "word": "bektore espazio"
    },
    {
      "code": "be",
      "lang": "Belarusian",
      "roman": "vjektarnaja prastóra",
      "sense": "mathematics",
      "tags": [
        "feminine"
      ],
      "word": "вектарная прастора"
    },
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "espai vectorial"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "sense": "mathematics",
      "word": "向量空間"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "xiàngliàng kōngjiān",
      "sense": "mathematics",
      "word": "向量空间"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "sense": "mathematics",
      "word": "矢量空間"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "shǐliàng kōngjiān",
      "sense": "mathematics",
      "word": "矢量空间"
    },
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "vektorový prostor"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "mathematics",
      "tags": [
        "neuter"
      ],
      "word": "vektorrum"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "mathematics",
      "tags": [
        "feminine"
      ],
      "word": "vectorruimte"
    },
    {
      "code": "eo",
      "lang": "Esperanto",
      "sense": "mathematics",
      "word": "vektora spaco"
    },
    {
      "code": "et",
      "lang": "Estonian",
      "sense": "mathematics",
      "word": "vektorruum"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "mathematics",
      "word": "vektoriavaruus"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "espace vectoriel"
    },
    {
      "code": "gl",
      "lang": "Galician",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "espazo vectorial"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "Vektorraum"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "dianysmatikós chóros",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "διανυσματικός χώρος"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "mathematics",
      "word": "vektortér"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "mathematics",
      "tags": [
        "neuter"
      ],
      "word": "vigurrúm"
    },
    {
      "code": "id",
      "lang": "Indonesian",
      "sense": "mathematics",
      "word": "ruang vektor"
    },
    {
      "code": "ia",
      "lang": "Interlingua",
      "sense": "mathematics",
      "word": "spatio vectorial"
    },
    {
      "code": "ga",
      "lang": "Irish",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "spás veicteoireach"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "spazio vettoriale"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "roman": "bekutoru kūkan",
      "sense": "mathematics",
      "word": "ベクトル空間"
    },
    {
      "code": "ko",
      "lang": "Korean",
      "roman": "bekteo gonggan",
      "sense": "mathematics",
      "word": "벡터 공간"
    },
    {
      "code": "ky",
      "lang": "Kyrgyz",
      "roman": "vektorduk meykindik",
      "sense": "mathematics",
      "word": "вектордук мейкиндик"
    },
    {
      "code": "lt",
      "lang": "Lithuanian",
      "sense": "mathematics",
      "tags": [
        "feminine"
      ],
      "word": "vektorinė erdvė"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "vektorski prostor",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "векторски простор"
    },
    {
      "code": "ms",
      "lang": "Malay",
      "sense": "mathematics",
      "word": "ruang vektor"
    },
    {
      "code": "ml",
      "lang": "Malayalam",
      "roman": "sadiśasamaṣṭi",
      "sense": "mathematics",
      "word": "സദിശസമഷ്ടി"
    },
    {
      "code": "no",
      "lang": "Norwegian",
      "sense": "mathematics",
      "tags": [
        "neuter"
      ],
      "word": "vektorrom"
    },
    {
      "code": "fa",
      "lang": "Persian",
      "sense": "mathematics",
      "word": "فضای برداری"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "mathematics",
      "tags": [
        "feminine"
      ],
      "word": "przestrzeń wektorowa"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "mathematics",
      "tags": [
        "feminine"
      ],
      "word": "przestrzeń liniowa"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "espaço vetorial"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "mathematics",
      "tags": [
        "neuter"
      ],
      "word": "spațiu vectorial"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "véktornoje prostránstvo",
      "sense": "mathematics",
      "tags": [
        "neuter"
      ],
      "word": "ве́кторное простра́нство"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "vektorski prostor"
    },
    {
      "code": "sk",
      "lang": "Slovak",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "vektorový priestor"
    },
    {
      "code": "sl",
      "lang": "Slovene",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "vektorski prostor"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "espacio vectorial"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "mathematics",
      "tags": [
        "neuter"
      ],
      "word": "vektorrum"
    },
    {
      "code": "tl",
      "lang": "Tagalog",
      "sense": "mathematics",
      "word": "espasyong bektor"
    },
    {
      "code": "ta",
      "lang": "Tamil",
      "roman": "ticaiyaṉ veḷi",
      "sense": "mathematics",
      "word": "திசையன் வெளி"
    },
    {
      "code": "th",
      "lang": "Thai",
      "sense": "mathematics",
      "word": "ปริภูมิเวกเตอร์"
    },
    {
      "code": "th",
      "lang": "Thai",
      "sense": "mathematics",
      "word": "ปริภูมิเชิงเส้น"
    },
    {
      "code": "tr",
      "lang": "Turkish",
      "sense": "mathematics",
      "word": "vektör uzayı"
    },
    {
      "code": "uk",
      "lang": "Ukrainian",
      "roman": "vektornyj prostir",
      "sense": "mathematics",
      "tags": [
        "masculine"
      ],
      "word": "векторний простір"
    },
    {
      "code": "vi",
      "lang": "Vietnamese",
      "sense": "mathematics",
      "word": "không gian vectơ"
    }
  ],
  "word": "vector space"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 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.