"Hodge star" meaning in English

{
  "etymology_text": "Introduced by W. V. D. Hodge.",
  "forms": [
    {
      "form": "Hodge stars",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Hodge star (plural Hodge stars)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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        },
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element."
      ],
      "id": "en-Hodge_star-en-noun-WaIwUohM",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "exterior",
          "exterior"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "oriented",
          "oriented"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "nondegenerate",
          "nondegenerate"
        ],
        [
          "symmetric",
          "symmetric"
        ],
        [
          "bilinear form",
          "bilinear form"
        ],
        [
          "Hodge dual",
          "Hodge dual"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "W. V. D. Hodge"
      ]
    }
  ],
  "word": "Hodge star"
}

{
  "etymology_text": "Introduced by W. V. D. Hodge.",
  "forms": [
    {
      "form": "Hodge stars",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Hodge star (plural Hodge stars)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
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        "English entries with language name categories using raw markup",
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        "English multiword terms",
        "English nouns",
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        "en:Mathematics"
      ],
      "glosses": [
        "A linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "exterior",
          "exterior"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "oriented",
          "oriented"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "nondegenerate",
          "nondegenerate"
        ],
        [
          "symmetric",
          "symmetric"
        ],
        [
          "bilinear form",
          "bilinear form"
        ],
        [
          "Hodge dual",
          "Hodge dual"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "W. V. D. Hodge"
      ]
    }
  ],
  "word": "Hodge star"
}