"matrix group" meaning in English

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      "form": "matrix groups",
      "tags": [
        "plural"
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      "expansion": "matrix group (plural matrix groups)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
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          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1976, S. Califano, Vibrational States, Wiley, page 112",
          "text": "The properties of matrix groups are of great importance for representation theory.",
          "type": "quotation"
        },
        {
          "text": "2011, László Babai, Finite Groups and Complexity Theory: From Leningrad to St Petersburg via Las Vegas, Alexander Kulikov, Nikolay Vereshchagin (editors), Computer Science – Theory and Applications: 6th International Computer Symposium, Springer, Lecture Notes in Computer Science 6651, page 162,\nThis paper is a personal account of the author's journey through the evolution of some of these interconnections, culminating in recent definitive results on the matrix group membership problem."
        },
        {
          "text": "2014, Peter Sarnak, Notes on thin matrix groups, Emmanuel Breuillard, Hee Oh (editors), Thin Groups and Superstrong Approximation, Cambridge University Press, page 343,\nApplications to diophantine problems on orbits of integer matrix groups, the affine sieve, group theory, gonality of curves and Heegaard genus of hyperbolic three manifolds, are given."
        }
      ],
      "glosses": [
        "Any group of invertible matrices over a specified field, with the group operation of matrix multiplication."
      ],
      "id": "en-matrix_group-en-noun-5J9EZyyv",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group"
        ],
        [
          "invertible matrices",
          "invertible matrix"
        ],
        [
          "field",
          "field"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "multiplication",
          "multiplication"
        ]
      ],
      "raw_glosses": [
        "(group theory) Any group of invertible matrices over a specified field, with the group operation of matrix multiplication."
      ],
      "related": [
        {
          "word": "unitary group"
        }
      ],
      "synonyms": [
        {
          "word": "linear group"
        }
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "rhymes": "-uːp"
    }
  ],
  "word": "matrix group"
}

{
  "forms": [
    {
      "form": "matrix groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "unitary group"
    }
  ],
  "senses": [
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      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
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        "Rhymes:English/uːp",
        "Rhymes:English/uːp/3 syllables",
        "en:Group theory"
      ],
      "examples": [
        {
          "ref": "1976, S. Califano, Vibrational States, Wiley, page 112",
          "text": "The properties of matrix groups are of great importance for representation theory.",
          "type": "quotation"
        },
        {
          "text": "2011, László Babai, Finite Groups and Complexity Theory: From Leningrad to St Petersburg via Las Vegas, Alexander Kulikov, Nikolay Vereshchagin (editors), Computer Science – Theory and Applications: 6th International Computer Symposium, Springer, Lecture Notes in Computer Science 6651, page 162,\nThis paper is a personal account of the author's journey through the evolution of some of these interconnections, culminating in recent definitive results on the matrix group membership problem."
        },
        {
          "text": "2014, Peter Sarnak, Notes on thin matrix groups, Emmanuel Breuillard, Hee Oh (editors), Thin Groups and Superstrong Approximation, Cambridge University Press, page 343,\nApplications to diophantine problems on orbits of integer matrix groups, the affine sieve, group theory, gonality of curves and Heegaard genus of hyperbolic three manifolds, are given."
        }
      ],
      "glosses": [
        "Any group of invertible matrices over a specified field, with the group operation of matrix multiplication."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group"
        ],
        [
          "invertible matrices",
          "invertible matrix"
        ],
        [
          "field",
          "field"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "multiplication",
          "multiplication"
        ]
      ],
      "raw_glosses": [
        "(group theory) Any group of invertible matrices over a specified field, with the group operation of matrix multiplication."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "rhymes": "-uːp"
    }
  ],
  "synonyms": [
    {
      "word": "linear group"
    }
  ],
  "word": "matrix group"
}

{
  "called_from": "linkages/371",
  "msg": "unrecognized linkage prefix: (group of invertible matrices): linear group desc=group of invertible matrices rest=linear group cls=romanization cls2=english e1=False e2=True",
  "path": [
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  "section": "English",
  "subsection": "noun",
  "title": "matrix group",
  "trace": ""
}