"inner product" meaning in English

{
  "forms": [
    {
      "form": "inner products",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "inner product (plural inner products)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Linear algebra",
          "orig": "en:Linear algebra",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "isoinner product"
        },
        {
          "word": "Petersson inner product"
        }
      ],
      "glosses": [
        "A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered."
      ],
      "id": "en-inner_product-en-noun-L9EJg4Ut",
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "generalization",
          "generalization"
        ],
        [
          "dot product",
          "dot product"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered."
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "da",
          "lang": "Danish",
          "sense": "generalization of the dot product",
          "tags": [
            "neuter"
          ],
          "word": "indre produkt"
        },
        {
          "code": "nl",
          "lang": "Dutch",
          "sense": "generalization of the dot product",
          "tags": [
            "neuter"
          ],
          "word": "inproduct"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "generalization of the dot product",
          "word": "sisätulo"
        },
        {
          "code": "hu",
          "lang": "Hungarian",
          "sense": "generalization of the dot product",
          "word": "belső szorzat"
        },
        {
          "code": "ja",
          "lang": "Japanese",
          "sense": "generalization of the dot product",
          "word": "内積"
        },
        {
          "code": "ko",
          "lang": "Korean",
          "roman": "naejeok",
          "sense": "generalization of the dot product",
          "word": "내적"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "generalization of the dot product",
          "word": "produs intern"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "generalization of the dot product",
          "word": "inre produkt"
        }
      ]
    }
  ],
  "word": "inner product"
}

{
  "derived": [
    {
      "word": "isoinner product"
    },
    {
      "word": "Petersson inner product"
    }
  ],
  "forms": [
    {
      "form": "inner products",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "inner product (plural inner products)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Linear algebra"
      ],
      "glosses": [
        "A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered."
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "generalization",
          "generalization"
        ],
        [
          "dot product",
          "dot product"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered."
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "da",
      "lang": "Danish",
      "sense": "generalization of the dot product",
      "tags": [
        "neuter"
      ],
      "word": "indre produkt"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "generalization of the dot product",
      "tags": [
        "neuter"
      ],
      "word": "inproduct"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "generalization of the dot product",
      "word": "sisätulo"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "generalization of the dot product",
      "word": "belső szorzat"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "sense": "generalization of the dot product",
      "word": "内積"
    },
    {
      "code": "ko",
      "lang": "Korean",
      "roman": "naejeok",
      "sense": "generalization of the dot product",
      "word": "내적"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "generalization of the dot product",
      "word": "produs intern"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "generalization of the dot product",
      "word": "inre produkt"
    }
  ],
  "word": "inner product"
}