"unitary group" meaning in English

{
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      "form": "unitary groups",
      "tags": [
        "plural"
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      "expansion": "unitary group (plural unitary groups)",
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  "lang_code": "en",
  "pos": "noun",
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          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
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      ],
      "derived": [
        {
          "word": "co-unitary group"
        },
        {
          "word": "projective unitary group"
        },
        {
          "word": "special unitary group"
        },
        {
          "word": "general unitary group"
        }
      ],
      "examples": [
        {
          "ref": "1995, Ruben Pauncz, The Symmetric Group in Quantum Chemistry, CRC Press, page 195:",
          "text": "The symmetric group is closely related to the unitary group.[…]The latest developments in spin free quantum chemistry have been the use of the unitary group for the calculation of the matrix elements of the Hamiltonian in the configuration interaction treatment.",
          "type": "quote"
        },
        {
          "ref": "2004, [1999], Shoon K. Kim, Group Theoretical Methods and Applications to Molecules and Crystals, Cambridge University Press, page 53:",
          "text": "Two of the most important types of groups that occur in physics are unitary groups and orthogonal groups.",
          "type": "quote"
        }
      ],
      "glosses": [
        "For given n, the group of n×n unitary matrices, with the group operation of matrix multiplication."
      ],
      "hyponyms": [
        {
          "word": "circle group"
        }
      ],
      "id": "en-unitary_group-en-noun-Wq4XowaR",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group#English"
        ],
        [
          "unitary matrices",
          "unitary matrix"
        ],
        [
          "matrix",
          "matrix#English"
        ],
        [
          "multiplication",
          "multiplication#English"
        ]
      ],
      "raw_glosses": [
        "(group theory) For given n, the group of n×n unitary matrices, with the group operation of matrix multiplication."
      ],
      "synonyms": [
        {
          "english": "especially over finite fields",
          "tags": [
            "obsolete"
          ],
          "word": "hyperorthogonal group"
        }
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "group of n×n unitary matrices",
          "word": "unitaarinen ryhmä"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "group of n×n unitary matrices",
          "tags": [
            "feminine"
          ],
          "word": "unitäre Gruppe"
        }
      ],
      "wikipedia": [
        "unitary group"
      ]
    }
  ],
  "word": "unitary group"
}

{
  "derived": [
    {
      "word": "co-unitary group"
    },
    {
      "word": "projective unitary group"
    },
    {
      "word": "special unitary group"
    },
    {
      "word": "general unitary group"
    }
  ],
  "forms": [
    {
      "form": "unitary groups",
      "tags": [
        "plural"
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      "word": "circle group"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        {
          "ref": "1995, Ruben Pauncz, The Symmetric Group in Quantum Chemistry, CRC Press, page 195:",
          "text": "The symmetric group is closely related to the unitary group.[…]The latest developments in spin free quantum chemistry have been the use of the unitary group for the calculation of the matrix elements of the Hamiltonian in the configuration interaction treatment.",
          "type": "quote"
        },
        {
          "ref": "2004, [1999], Shoon K. Kim, Group Theoretical Methods and Applications to Molecules and Crystals, Cambridge University Press, page 53:",
          "text": "Two of the most important types of groups that occur in physics are unitary groups and orthogonal groups.",
          "type": "quote"
        }
      ],
      "glosses": [
        "For given n, the group of n×n unitary matrices, with the group operation of matrix multiplication."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group#English"
        ],
        [
          "unitary matrices",
          "unitary matrix"
        ],
        [
          "matrix",
          "matrix#English"
        ],
        [
          "multiplication",
          "multiplication#English"
        ]
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      "raw_glosses": [
        "(group theory) For given n, the group of n×n unitary matrices, with the group operation of matrix multiplication."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "unitary group"
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  ],
  "synonyms": [
    {
      "english": "especially over finite fields",
      "tags": [
        "obsolete"
      ],
      "word": "hyperorthogonal group"
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "group of n×n unitary matrices",
      "word": "unitaarinen ryhmä"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "group of n×n unitary matrices",
      "tags": [
        "feminine"
      ],
      "word": "unitäre Gruppe"
    }
  ],
  "word": "unitary group"
}