"tensor product" meaning in English

{
  "forms": [
    {
      "form": "tensor products",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "tensor product (plural tensor 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": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2004, David S. Dummit with Richard M. Foote, chapter 11, in Abstract Algebra, →OCLC, page 421",
          "text": "Linear Transformations on Tensor Products of Vector Spaces\n…\nProposition 16. Let V and W be finite dimensional vector spaces over the field F with bases v_1,...,v_n and w_1,...,w_m respectively. Then V⊗_FW is a vector space over F of dimension nm with basis v_i⊗w_j, 1<i<n and 1<j<m.",
          "type": "quotation"
        },
        {
          "ref": "2012, 27:30 from the start, in Lecture 1 . Hopf Algebras and Combinatorics (Federico Ardila), spoken by Federico Ardila (Federico Ardila), Federico Ardila, via YouTube",
          "text": "[The tensor product] U⊗V is the span of u⊗v:u∈U,v∈V\nmodulo the relations\n·u⊗(v+v')=u⊗v+u⊗v'\\·(u+u')⊗v=u⊗v+u'⊗v\\·(λu)⊗v=λ(u⊗v)=u⊗(λv)",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗."
      ],
      "holonyms": [
        {
          "word": "monoidal category"
        }
      ],
      "hyponyms": [
        {
          "word": "Kronecker product"
        },
        {
          "word": "exterior product"
        },
        {
          "word": "wedge product"
        }
      ],
      "id": "en-tensor_product-en-noun-ceYOrAVT",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "bilinear",
          "bilinear"
        ],
        [
          "operation",
          "operation"
        ],
        [
          "vector",
          "vector"
        ],
        [
          "matrices",
          "matrix"
        ],
        [
          "tensor",
          "tensor"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "topological",
          "topological"
        ],
        [
          "module",
          "module"
        ],
        [
          "⊗",
          "⊗"
        ]
      ],
      "meronyms": [
        {
          "english": "if the tensor product is between algebraic structures",
          "word": "tensor"
        }
      ],
      "raw_glosses": [
        "(mathematics) The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "et",
          "lang": "Estonian",
          "sense": "bilinear operation",
          "word": "tensorkorrutis"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "bilinear operation",
          "word": "tensoritulo"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "bilinear operation",
          "tags": [
            "masculine"
          ],
          "word": "produit tensoriel"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "bilinear operation",
          "tags": [
            "neuter"
          ],
          "word": "Tensorprodukt"
        },
        {
          "code": "ja",
          "lang": "Japanese",
          "roman": "tensoru-seki",
          "sense": "bilinear operation",
          "word": "テンソル積"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "bilinear operation",
          "tags": [
            "neuter"
          ],
          "word": "produs tensorial"
        }
      ],
      "wikipedia": [
        "tensor product"
      ]
    }
  ],
  "word": "tensor product"
}

{
  "forms": [
    {
      "form": "tensor products",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "tensor product (plural tensor products)",
      "name": "en-noun"
    }
  ],
  "holonyms": [
    {
      "word": "monoidal category"
    }
  ],
  "hyponyms": [
    {
      "word": "Kronecker product"
    },
    {
      "word": "exterior product"
    },
    {
      "word": "wedge product"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "english": "if the tensor product is between algebraic structures",
      "word": "tensor"
    }
  ],
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2004, David S. Dummit with Richard M. Foote, chapter 11, in Abstract Algebra, →OCLC, page 421",
          "text": "Linear Transformations on Tensor Products of Vector Spaces\n…\nProposition 16. Let V and W be finite dimensional vector spaces over the field F with bases v_1,...,v_n and w_1,...,w_m respectively. Then V⊗_FW is a vector space over F of dimension nm with basis v_i⊗w_j, 1<i<n and 1<j<m.",
          "type": "quotation"
        },
        {
          "ref": "2012, 27:30 from the start, in Lecture 1 . Hopf Algebras and Combinatorics (Federico Ardila), spoken by Federico Ardila (Federico Ardila), Federico Ardila, via YouTube",
          "text": "[The tensor product] U⊗V is the span of u⊗v:u∈U,v∈V\nmodulo the relations\n·u⊗(v+v')=u⊗v+u⊗v'\\·(u+u')⊗v=u⊗v+u'⊗v\\·(λu)⊗v=λ(u⊗v)=u⊗(λv)",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "bilinear",
          "bilinear"
        ],
        [
          "operation",
          "operation"
        ],
        [
          "vector",
          "vector"
        ],
        [
          "matrices",
          "matrix"
        ],
        [
          "tensor",
          "tensor"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "algebra",
          "algebra"
        ],
        [
          "topological",
          "topological"
        ],
        [
          "module",
          "module"
        ],
        [
          "⊗",
          "⊗"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "tensor product"
      ]
    }
  ],
  "translations": [
    {
      "code": "et",
      "lang": "Estonian",
      "sense": "bilinear operation",
      "word": "tensorkorrutis"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "bilinear operation",
      "word": "tensoritulo"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "bilinear operation",
      "tags": [
        "masculine"
      ],
      "word": "produit tensoriel"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "bilinear operation",
      "tags": [
        "neuter"
      ],
      "word": "Tensorprodukt"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "roman": "tensoru-seki",
      "sense": "bilinear operation",
      "word": "テンソル積"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "bilinear operation",
      "tags": [
        "neuter"
      ],
      "word": "produs tensorial"
    }
  ],
  "word": "tensor product"
}