"eigenvector" meaning in All languages combined

See eigenvector on Wiktionary

Noun [Dutch]

IPA: /ˈɛi̯.ɣənˌvɛk.tɔr/ Audio: Nl-eigenvector.ogg Forms: eigenvectoren [plural]
Etymology: From eigen + vector, calque of German Eigenvektor. Etymology templates: {{compound|nl|eigen|vector}} eigen + vector, {{calque|nl|de|Eigenvektor|nocap=1}} calque of German Eigenvektor Head templates: {{nl-noun|m|-:en|-}} eigenvector m (plural eigenvectoren)
  1. (linear algebra) eigenvector Tags: masculine Categories (topical): Linear algebra

Noun [English]

Audio: en-us-eigenvector.ogg [US] Forms: eigenvectors [plural]
Etymology: eigen- + vector, a partial calque of German Eigenvektor. The prefix eigen- (also used in eigenvalue) was first used in 1904, by David Hilbert, and was possibly inspired by a related usage by Hermann von Helmholtz. Etymology templates: {{prefix|en|eigen|vector}} eigen- + vector, {{partial translation|en|de|Eigenvektor|nocap=1}} partial calque of German Eigenvektor, {{m|en|eigen-}} eigen-, {{m|en|eigenvalue}} eigenvalue Head templates: {{en-noun}} eigenvector (plural eigenvectors)
  1. (linear algebra) A vector that is not rotated under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue). Categories (topical): Linear algebra Synonyms: characteristic vector, latent vector, proper vector Translations (vector not rotated by linear transformation): 本徵向量 (Chinese Mandarin), 本征向量 (běnzhēng xiàngliàng) (Chinese Mandarin), 特徵向量 (Chinese Mandarin), 特征向量 (tèzhēng xiàngliàng) (Chinese Mandarin), egenvektor [common-gender] (Danish), eigenvector [masculine] (Dutch), omavektor (Estonian), ominaisvektori (Finnish), vecteur propre [masculine] (French), Eigenvektor [masculine] (German), ιδιοδιάνυσμα (idiodiánysma) [neuter] (Greek), וֶקְטוֹר עַצְמִי [masculine] (Hebrew), eiginvigur [masculine] (Icelandic), eiginvektor [masculine] (Icelandic), autovettore [masculine] (Italian), 固有ベクトル (koyū bekutoru) (Japanese), egenvektor [masculine] (Norwegian Bokmål), eigenvektor [masculine] (Norwegian Nynorsk), wektor własny [masculine] (Polish), autovetor [masculine] (Portuguese), vetor próprio [masculine] (Portuguese), vector propriu [masculine] (Romanian), со́бственный ве́ктор (sóbstvennyj véktor) [masculine] (Russian), vector propio [masculine] (Spanish), autovector [masculine] (Spanish), egenvektor [common-gender] (Swedish)
    Sense id: en-eigenvector-en-noun-N-CaCqp8 Categories (other): English entries with language name categories using raw markup, English hybridisms, English terms prefixed with eigen- Disambiguation of English entries with language name categories using raw markup: 49 51 Disambiguation of English hybridisms: 45 55 Disambiguation of English terms prefixed with eigen-: 52 48 Topics: linear-algebra, mathematics, sciences Disambiguation of 'vector not rotated by linear transformation': 80 20
  2. (physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A." Categories (topical): Engineering, Physics
    Sense id: en-eigenvector-en-noun-Em-6LoGs Categories (other): English entries with incorrect language header, English entries with language name categories using raw markup, English hybridisms, English terms prefixed with eigen- Disambiguation of English entries with incorrect language header: 44 56 Disambiguation of English entries with language name categories using raw markup: 49 51 Disambiguation of English hybridisms: 45 55 Disambiguation of English terms prefixed with eigen-: 52 48 Topics: engineering, natural-sciences, physical-sciences, physics
The following are not (yet) sense-disambiguated
Derived forms: eigenvectorial, eigenbivector, left eigenvector, right eigenvector

Noun [Spanish]

Forms: eigenvectores [plural]
Head templates: {{es-noun|m}} eigenvector m (plural eigenvectores)
  1. (linear algebra) eigenvector Tags: masculine Categories (topical): Linear algebra Synonyms: autovector, vector propio
    Sense id: en-eigenvector-es-noun-wLpIpS6V Categories (other): Spanish entries with incorrect language header Topics: linear-algebra, mathematics, sciences

Inflected forms

Download JSON data for eigenvector meaning in All languages combined (12.1kB)

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      "_dis1": "0 0",
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          "sense": "vector not rotated by linear transformation",
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          "_dis1": "80 20",
          "code": "ja",
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          "word": "固有ベクトル"
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        "1": "nl",
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        "3": "Eigenvektor",
        "nocap": "1"
      },
      "expansion": "calque of German Eigenvektor",
      "name": "calque"
    }
  ],
  "etymology_text": "From eigen + vector, calque of German Eigenvektor.",
  "forms": [
    {
      "form": "eigenvectoren",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "m",
        "2": "-:en",
        "3": "-"
      },
      "expansion": "eigenvector m (plural eigenvectoren)",
      "name": "nl-noun"
    }
  ],
  "hyphenation": [
    "ei‧gen‧vec‧tor"
  ],
  "lang": "Dutch",
  "lang_code": "nl",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "Dutch compound terms",
        "Dutch entries with incorrect language header",
        "Dutch lemmas",
        "Dutch masculine nouns",
        "Dutch nouns",
        "Dutch nouns with lengthened vowel in the plural",
        "Dutch nouns with plural in -en",
        "Dutch terms calqued from German",
        "Dutch terms derived from German",
        "Dutch terms with IPA pronunciation",
        "Dutch terms with audio links",
        "nl:Linear algebra"
      ],
      "glosses": [
        "eigenvector"
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "eigenvector",
          "eigenvector#English"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) eigenvector"
      ],
      "tags": [
        "masculine"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈɛi̯.ɣənˌvɛk.tɔr/"
    },
    {
      "audio": "Nl-eigenvector.ogg",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/0/04/Nl-eigenvector.ogg/Nl-eigenvector.ogg.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/0/04/Nl-eigenvector.ogg",
      "text": "Audio"
    }
  ],
  "word": "eigenvector"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English entries with language name categories using raw markup",
    "English hybridisms",
    "English lemmas",
    "English nouns",
    "English terms derived from German",
    "English terms partially calqued from German",
    "English terms prefixed with eigen-",
    "English terms with audio links"
  ],
  "derived": [
    {
      "word": "eigenvectorial"
    },
    {
      "word": "eigenbivector"
    },
    {
      "word": "left eigenvector"
    },
    {
      "word": "right eigenvector"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "eigen",
        "3": "vector"
      },
      "expansion": "eigen- + vector",
      "name": "prefix"
    },
    {
      "args": {
        "1": "en",
        "2": "de",
        "3": "Eigenvektor",
        "nocap": "1"
      },
      "expansion": "partial calque of German Eigenvektor",
      "name": "partial translation"
    },
    {
      "args": {
        "1": "en",
        "2": "eigen-"
      },
      "expansion": "eigen-",
      "name": "m"
    },
    {
      "args": {
        "1": "en",
        "2": "eigenvalue"
      },
      "expansion": "eigenvalue",
      "name": "m"
    }
  ],
  "etymology_text": "eigen- + vector, a partial calque of German Eigenvektor.\nThe prefix eigen- (also used in eigenvalue) was first used in 1904, by David Hilbert, and was possibly inspired by a related usage by Hermann von Helmholtz.",
  "forms": [
    {
      "form": "eigenvectors",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "eigenvector (plural eigenvectors)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "eigenbasis"
    },
    {
      "word": "eigenbrain"
    },
    {
      "word": "eigendecomposition"
    },
    {
      "word": "eigenface"
    },
    {
      "word": "eigenfunction"
    },
    {
      "word": "eigenhead"
    },
    {
      "word": "eigenmode"
    },
    {
      "word": "eigenpair"
    },
    {
      "word": "eigenspace"
    },
    {
      "word": "eigenspinor"
    },
    {
      "word": "eigenstate"
    },
    {
      "word": "eigensystem"
    },
    {
      "word": "eigentheory"
    },
    {
      "word": "eigenvalue"
    },
    {
      "urls": [
        "http://mathworld.wolfram.com/Eigenvector.html"
      ],
      "word": "Mathworld article on eigenvectors"
    }
  ],
  "senses": [
    {
      "categories": [
        "en:Linear algebra"
      ],
      "glosses": [
        "A vector that is not rotated under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue)."
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "vector",
          "vector"
        ],
        [
          "linear transformation",
          "linear transformation"
        ],
        [
          "left",
          "left eigenvector"
        ],
        [
          "right eigenvector",
          "right eigenvector"
        ],
        [
          "scalar",
          "scalar"
        ],
        [
          "eigenvalue",
          "eigenvalue"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) A vector that is not rotated under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue)."
      ],
      "synonyms": [
        {
          "word": "characteristic vector"
        },
        {
          "word": "latent vector"
        },
        {
          "word": "proper vector"
        }
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Engineering",
        "en:Physics"
      ],
      "glosses": [
        "A right eigenvector; given a matrix A, the eigenvector of the transformation \"left-side multiplication by A.\""
      ],
      "links": [
        [
          "physics",
          "physics"
        ],
        [
          "engineering",
          "engineering#Noun"
        ],
        [
          "right eigenvector",
          "right eigenvector"
        ],
        [
          "matrix",
          "matrix"
        ]
      ],
      "raw_glosses": [
        "(physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation \"left-side multiplication by A.\""
      ],
      "topics": [
        "engineering",
        "natural-sciences",
        "physical-sciences",
        "physics"
      ]
    }
  ],
  "sounds": [
    {
      "audio": "en-us-eigenvector.ogg",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/e/e8/En-us-eigenvector.ogg/En-us-eigenvector.ogg.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/e/e8/En-us-eigenvector.ogg",
      "tags": [
        "US"
      ],
      "text": "Audio (US)"
    }
  ],
  "translations": [
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "sense": "vector not rotated by linear transformation",
      "word": "本徵向量"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "běnzhēng xiàngliàng",
      "sense": "vector not rotated by linear transformation",
      "word": "本征向量"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "sense": "vector not rotated by linear transformation",
      "word": "特徵向量"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "tèzhēng xiàngliàng",
      "sense": "vector not rotated by linear transformation",
      "word": "特征向量"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "common-gender"
      ],
      "word": "egenvektor"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "eigenvector"
    },
    {
      "code": "et",
      "lang": "Estonian",
      "sense": "vector not rotated by linear transformation",
      "word": "omavektor"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "vector not rotated by linear transformation",
      "word": "ominaisvektori"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "vecteur propre"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "Eigenvektor"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "idiodiánysma",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "neuter"
      ],
      "word": "ιδιοδιάνυσμα"
    },
    {
      "code": "he",
      "lang": "Hebrew",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "וֶקְטוֹר עַצְמִי"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "eiginvigur"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "eiginvektor"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "autovettore"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "roman": "koyū bekutoru",
      "sense": "vector not rotated by linear transformation",
      "word": "固有ベクトル"
    },
    {
      "code": "no",
      "lang": "Norwegian Bokmål",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "egenvektor"
    },
    {
      "code": "no",
      "lang": "Norwegian Nynorsk",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "eigenvektor"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "wektor własny"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "autovetor"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "vetor próprio"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "vector propriu"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "sóbstvennyj véktor",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "со́бственный ве́ктор"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "vector propio"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "masculine"
      ],
      "word": "autovector"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "vector not rotated by linear transformation",
      "tags": [
        "common-gender"
      ],
      "word": "egenvektor"
    }
  ],
  "wikipedia": [
    "David Hilbert",
    "Hermann von Helmholtz",
    "eigenvector"
  ],
  "word": "eigenvector"
}

{
  "forms": [
    {
      "form": "eigenvectores",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "m"
      },
      "expansion": "eigenvector m (plural eigenvectores)",
      "name": "es-noun"
    }
  ],
  "lang": "Spanish",
  "lang_code": "es",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "Spanish countable nouns",
        "Spanish entries with incorrect language header",
        "Spanish lemmas",
        "Spanish masculine nouns",
        "Spanish nouns",
        "es:Linear algebra"
      ],
      "glosses": [
        "eigenvector"
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "eigenvector",
          "eigenvector#English"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) eigenvector"
      ],
      "synonyms": [
        {
          "word": "autovector"
        },
        {
          "word": "vector propio"
        }
      ],
      "tags": [
        "masculine"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "eigenvector"
}

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.