"eigenelement" meaning in English

See eigenelement in All languages combined, or Wiktionary

Noun

Forms: eigenelements [plural]
Head templates: {{en-noun}} eigenelement (plural eigenelements)
  1. (mathematics) A nonzero element m of a semimodule M, such that there exists an endomorphism A on M and a real number r (a corresponding eigenvalue) for which the image of m under A is equal to the product of r times m; i.e. mA=rm. Categories (topical): Mathematics
    Sense id: en-eigenelement-en-noun-O0Hjzk-i Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: mathematics, sciences

Inflected forms

{
  "forms": [
    {
      "form": "eigenelements",
      "tags": [
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      ]
    }
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  "head_templates": [
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      "args": {},
      "expansion": "eigenelement (plural eigenelements)",
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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          "source": "w"
        },
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        },
        {
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          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A nonzero element m of a semimodule M, such that there exists an endomorphism A on M and a real number r (a corresponding eigenvalue) for which the image of m under A is equal to the product of r times m; i.e. mA=rm."
      ],
      "id": "en-eigenelement-en-noun-O0Hjzk-i",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "nonzero",
          "nonzero"
        ],
        [
          "semimodule",
          "semimodule"
        ],
        [
          "endomorphism",
          "endomorphism"
        ],
        [
          "eigenvalue",
          "eigenvalue"
        ],
        [
          "image",
          "image"
        ],
        [
          "product",
          "product"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A nonzero element m of a semimodule M, such that there exists an endomorphism A on M and a real number r (a corresponding eigenvalue) for which the image of m under A is equal to the product of r times m; i.e. mA=rm."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "eigenelement"
}
{
  "forms": [
    {
      "form": "eigenelements",
      "tags": [
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    }
  ],
  "head_templates": [
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        "English entries with incorrect language header",
        "English lemmas",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "glosses": [
        "A nonzero element m of a semimodule M, such that there exists an endomorphism A on M and a real number r (a corresponding eigenvalue) for which the image of m under A is equal to the product of r times m; i.e. mA=rm."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
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          "nonzero",
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          "semimodule",
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        ],
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          "endomorphism",
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        ],
        [
          "eigenvalue",
          "eigenvalue"
        ],
        [
          "image",
          "image"
        ],
        [
          "product",
          "product"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A nonzero element m of a semimodule M, such that there exists an endomorphism A on M and a real number r (a corresponding eigenvalue) for which the image of m under A is equal to the product of r times m; i.e. mA=rm."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
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}

Download raw JSONL data for eigenelement meaning in English (1.1kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.

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