"eigenfunction" meaning in All languages combined

See eigenfunction on Wiktionary

Noun [English]

Forms: eigenfunctions [plural]
Etymology: Etymology tree Proto-Indo-European *h₂eyḱ- Proto-Indo-European *h₂eh₂óyḱe Proto-Germanic *aiganą Proto-Germanic *aiganaz Proto-West Germanic *aigan Old High German eigan Middle High German eigen German eigenbor. English eigen- Old French fonction Middle French functionbor. English function English eigenfunction From eigen- + function. Etymology templates: {{ety|en|:af|eigen-|function|text=+|tree=1}} Etymology tree Proto-Indo-European *h₂eyḱ- Proto-Indo-European *h₂eh₂óyḱe Proto-Germanic *aiganą Proto-Germanic *aiganaz Proto-West Germanic *aigan Old High German eigan Middle High German eigen German eigenbor. English eigen- Old French fonction Middle French functionbor. English function English eigenfunction [Appendix:Glossary#loanword|Borrowed]] from", "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "id" : "participle", "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "children" : [ { "terms" : [ { "id" : "own", "children" : [ { "terms" : [ { "id" : "obtain", "children" : [ ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*h₂eyḱ-", "lang" : "ine-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*h₂eh₂óyḱe", "lang" : "ine-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Proto-Germanic", "term" : "*aiganą", "status" : "ok", "lang" : "gem-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "lang_name" : "Proto-Germanic", "term" : "*aiganaz", "status" : "ok", "lang" : "gem-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Proto-West Germanic", "term" : "*aigan", "lang" : "gmw-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Old High German", "term" : "eigan", "status" : "ok", "lang" : "goh" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Middle High German", "term" : "eigen", "status" : "inline", "lang" : "gmh" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "German", "term" : "eigen", "status" : "ok", "lang" : "de" } ], "keyword" : "bor" } ], "lang_name" : "English", "term" : "eigen-", "status" : "ok", "lang" : "en" }, { "children" : [ { "keyword_abbrev" : "bor.", "keyword_label" : "Borrowed from", "terms" : [ { "children" : [ { "terms" : [ { "children" : [ ], "lang_name" : "Old French", "term" : "fonction", "status" : "missing", "lang" : "fro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Middle French", "term" : "function", "status" : "ok", "lang" : "frm" } ], "keyword" : "bor" } ], "lang_name" : "English", "term" : "function", "status" : "ok", "lang" : "en" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "lang_name" : "English", "term" : "eigenfunction", "status" : "ok", "lang" : "en" }" data-lang="en" data-title="eigenfunction"> From eigen- + function. Head templates: {{en-noun}} eigenfunction (plural eigenfunctions)
  1. (mathematics) A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue). Synonyms: proper function, eigenstate Translations (function): 本徵函數 /本征函数 (běnzhēng hánshù) (Chinese Mandarin), ominaisfunktio (Finnish), fonction propre [feminine] (French), Eigenfunktion [feminine] (German), ιδιοσυνάρτηση (idiosynártisi) [feminine] (Greek), eiginfall [neuter] (Icelandic), autofunzione [feminine] (Italian), 固有関数 (koyū kansū) (Japanese), autofunção [Brazil, feminine] (Portuguese), função própria [Portugal, feminine] (Portuguese), со́бственная фу́нкция (sóbstvennaja fúnkcija) [feminine] (Russian), autofunción [feminine] (Spanish), función propia [feminine] (Spanish), egenfunktion [common-gender] (Swedish), ffwythiant eigen [masculine] (Welsh)

Inflected forms

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    },
    {
      "word": "hamiltonian"
    }
  ],
  "senses": [
    {
      "categories": [
        "Arabic terms with non-redundant manual transliterations",
        "English countable nouns",
        "English entries with etymology texts",
        "English entries with etymology trees",
        "English entries with incorrect language header",
        "English lemmas",
        "English nouns",
        "English terms prefixed with eigen-",
        "English terms with quotations",
        "Entries with translation boxes",
        "Mandarin terms with redundant transliterations",
        "Pages using etymon with no ID",
        "Pages with 1 entry",
        "Pages with entries",
        "Pages with etymology trees",
        "Requests for review of Arabic translations",
        "Terms with Arabic translations",
        "Terms with Finnish translations",
        "Terms with French translations",
        "Terms with German translations",
        "Terms with Greek translations",
        "Terms with Icelandic translations",
        "Terms with Italian translations",
        "Terms with Japanese translations",
        "Terms with Mandarin translations",
        "Terms with Portuguese translations",
        "Terms with Russian translations",
        "Terms with Spanish translations",
        "Terms with Swedish translations",
        "Terms with Welsh translations",
        "en:Functions",
        "en:Mathematics"
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              98,
              112
            ],
            [
              215,
              229
            ]
          ],
          "ref": "2000, John von Neumann, E. Wigner, “On the Behaviour of Eigenvalues in Adiabatic Processes”, in Hinne Hettema, transl., edited by Hinne Hettema, Quantum Chemistry: Classic Scientific Papers, World Scientific, published 1929, page 25:",
          "text": "For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters. The case in which one knows the eigenvalues and eigenfunctions for two special values of the parameters, and is interested in the region in between is particularly interesting.",
          "type": "quotation"
        },
        {
          "bold_text_offsets": [
            [
              58,
              72
            ]
          ],
          "ref": "2005, Leonid D. Akulenko, Sergei V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications, CRC Press (Chapman & Hall), page 1:",
          "text": "Problems that require an investigation of eigenvalues and eigenfunctions arise in connection with numerous topics in mechanics, the theory of vibrations and stability, hydrodynamics, elasticity, acoustics, electrodynamics, quantum mechanics, etc.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "function",
          "function"
        ],
        [
          "linear",
          "linear"
        ],
        [
          "operator",
          "operator"
        ],
        [
          "scalar",
          "scalar"
        ],
        [
          "eigenvalue",
          "eigenvalue"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue)."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "proper function"
    },
    {
      "word": "eigenstate"
    }
  ],
  "translations": [
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "lang_code": "cmn",
      "roman": "běnzhēng hánshù",
      "sense": "function",
      "word": "本徵函數 /本征函数"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "lang_code": "fi",
      "sense": "function",
      "word": "ominaisfunktio"
    },
    {
      "code": "fr",
      "lang": "French",
      "lang_code": "fr",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "fonction propre"
    },
    {
      "code": "de",
      "lang": "German",
      "lang_code": "de",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "Eigenfunktion"
    },
    {
      "code": "el",
      "lang": "Greek",
      "lang_code": "el",
      "roman": "idiosynártisi",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "ιδιοσυνάρτηση"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "lang_code": "is",
      "sense": "function",
      "tags": [
        "neuter"
      ],
      "word": "eiginfall"
    },
    {
      "code": "it",
      "lang": "Italian",
      "lang_code": "it",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "autofunzione"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "lang_code": "ja",
      "roman": "koyū kansū",
      "sense": "function",
      "word": "固有関数"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "lang_code": "pt",
      "sense": "function",
      "tags": [
        "Brazil",
        "feminine"
      ],
      "word": "autofunção"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "lang_code": "pt",
      "sense": "function",
      "tags": [
        "Portugal",
        "feminine"
      ],
      "word": "função própria"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "lang_code": "ru",
      "roman": "sóbstvennaja fúnkcija",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "со́бственная фу́нкция"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "lang_code": "es",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "autofunción"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "lang_code": "es",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "función propia"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "lang_code": "sv",
      "sense": "function",
      "tags": [
        "common-gender"
      ],
      "word": "egenfunktion"
    },
    {
      "code": "cy",
      "lang": "Welsh",
      "lang_code": "cy",
      "sense": "function",
      "tags": [
        "masculine"
      ],
      "word": "ffwythiant eigen"
    }
  ],
  "word": "eigenfunction"
}

Download raw JSONL data for eigenfunction meaning in All languages combined (8.8kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2026-06-07 from the enwiktionary dump dated 2026-06-01 using wiktextract (e79dea5 and 7f4db16). 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.