"eigenvector" meaning in English

See eigenvector in All languages combined, or Wiktionary

Noun

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

Inflected forms

Download JSON data for eigenvector meaning in English (9.4kB)

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      "code": "cmn",
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      "roman": "běnzhēng xiàngliàng",
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      "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"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-12 from the enwiktionary dump dated 2024-05-02 using wiktextract (ae36afe and 304864d). 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.