"special unitary group" meaning in English

{
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      "form": "special unitary groups",
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      "expansion": "special unitary group (plural special 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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      "examples": [
        {
          "text": "1992 [Prentice-Hall], George H. Duffey, Applied Group Theory: For Physicists and Chemists, 2015, Dover, Unabridged Republication, page 284,\nThe special unitary group in two dimensions is represented by the 2 X 2 unitary matrices whose determinants equal 1."
        },
        {
          "ref": "2000, Herbert S. Green, Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process, Springer, page 26",
          "text": "The group is called the special unitary group in two dimensions, or SU(2), because it acts on matrices of degree 2.",
          "type": "quotation"
        },
        {
          "text": "2004, Roger Cooke (translator), Vladimir I. Arnold, Lectures on Partial Differential Equations, [1997, Lekstii ob uravneniyakh s chastnymi proizvodnymi], Springer, page 81, When n = 3, the group of rotations SO(3) is isomorphic to the real three-dimensional projective space ℝP³. It has a two-sheeted covering by the three-dimensional sphere (the group of unit quaternions), which in turn is isomorphic to the special unitary group SU(2), also known as the spin group of order 3, as in the following diagram"
        }
      ],
      "glosses": [
        "For given n, the group of n×n unitary matrices with complex elements and determinant equal to one."
      ],
      "id": "en-special_unitary_group-en-noun-jNDDn73F",
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          "linear algebra",
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        [
          "unitary matrices",
          "unitary matrix"
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          "determinant"
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      "raw_glosses": [
        "(linear algebra, group theory) For given n, the group of n×n unitary matrices with complex elements and determinant equal to one."
      ],
      "topics": [
        "group-theory",
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "group of n×n matrices with complex elements and determinant 1",
          "word": "erityinen unitaarinen ryhmä"
        }
      ]
    }
  ],
  "word": "special unitary group"
}

{
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    {
      "form": "special unitary groups",
      "tags": [
        "plural"
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        "en:Linear algebra"
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      "examples": [
        {
          "text": "1992 [Prentice-Hall], George H. Duffey, Applied Group Theory: For Physicists and Chemists, 2015, Dover, Unabridged Republication, page 284,\nThe special unitary group in two dimensions is represented by the 2 X 2 unitary matrices whose determinants equal 1."
        },
        {
          "ref": "2000, Herbert S. Green, Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process, Springer, page 26",
          "text": "The group is called the special unitary group in two dimensions, or SU(2), because it acts on matrices of degree 2.",
          "type": "quotation"
        },
        {
          "text": "2004, Roger Cooke (translator), Vladimir I. Arnold, Lectures on Partial Differential Equations, [1997, Lekstii ob uravneniyakh s chastnymi proizvodnymi], Springer, page 81, When n = 3, the group of rotations SO(3) is isomorphic to the real three-dimensional projective space ℝP³. It has a two-sheeted covering by the three-dimensional sphere (the group of unit quaternions), which in turn is isomorphic to the special unitary group SU(2), also known as the spin group of order 3, as in the following diagram"
        }
      ],
      "glosses": [
        "For given n, the group of n×n unitary matrices with complex elements and determinant equal to one."
      ],
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          "linear algebra"
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          "group theory",
          "group theory"
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        [
          "unitary matrices",
          "unitary matrix"
        ],
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          "determinant"
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      "raw_glosses": [
        "(linear algebra, group theory) For given n, the group of n×n unitary matrices with complex elements and determinant equal to one."
      ],
      "topics": [
        "group-theory",
        "linear-algebra",
        "mathematics",
        "sciences"
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  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "group of n×n matrices with complex elements and determinant 1",
      "word": "erityinen unitaarinen ryhmä"
    }
  ],
  "word": "special unitary group"
}