"adjoint" meaning in English

{
  "derived": [
    {
      "_dis1": "0 0 0",
      "word": "adjointable"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjoint action"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjoint curve"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjoint endomorphism"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjoint functor"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjointly"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjoint matrix"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjointness"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjoint operator"
    },
    {
      "_dis1": "0 0 0",
      "word": "adjoint representation"
    },
    {
      "_dis1": "0 0 0",
      "word": "left adjoint functor"
    },
    {
      "_dis1": "0 0 0",
      "word": "nonadjoint"
    },
    {
      "_dis1": "0 0 0",
      "word": "right adjoint functor"
    }
  ],
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        "2": "fr",
        "3": "adjoindre",
        "4": "",
        "5": "to join"
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      "expansion": "French adjoindre (“to join”)",
      "name": "der"
    },
    {
      "args": {
        "1": "en",
        "2": "adjunct"
      },
      "expansion": "Doublet of adjunct",
      "name": "doublet"
    }
  ],
  "etymology_text": "From French adjoindre (“to join”), from late 19th C; see also adjoin. Doublet of adjunct.\nIn the case of category theory (which brings together concepts from numerous fields), the term is often confounded with adjunct and the relationship is called an adjunction. The origin of any particular usage may therefore be uncertain.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "adjoint (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "related": [
    {
      "_dis1": "0 0 0",
      "tags": [
        "noun"
      ],
      "word": "adjunction"
    },
    {
      "_dis1": "0 0 0",
      "word": "coadjoint"
    },
    {
      "_dis1": "0 0 0",
      "word": "self-adjoint"
    },
    {
      "_dis1": "0 0 0",
      "word": "sub-adjoint"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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        }
      ],
      "glosses": [
        "Used in certain contexts, in each case involving a pair of transformations, one of which is, or is analogous to, conjugation (either inner automorphism or complex conjugation)."
      ],
      "id": "en-adjoint-en-adj-2XMS~uaM",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "conjugation",
          "conjugate#English"
        ],
        [
          "inner automorphism",
          "inner automorphism#English"
        ],
        [
          "complex conjugation",
          "complex conjugation#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Used in certain contexts, in each case involving a pair of transformations, one of which is, or is analogous to, conjugation (either inner automorphism or complex conjugation)."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
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      ],
      "glosses": [
        "That is related to another functor by an adjunction."
      ],
      "id": "en-adjoint-en-adj-L6jDT~hH",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "category theory",
          "category theory"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "adjunction",
          "adjunction"
        ]
      ],
      "raw_glosses": [
        "(mathematics, category theory, of a functor) That is related to another functor by an adjunction."
      ],
      "raw_tags": [
        "of a functor"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    },
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      ],
      "examples": [
        {
          "ref": "1933, H. F. Baker, Principles of Geometry, volume 5, published 2010, page 103:",
          "text": "The sets A + A₀, B + B₀, together, form the complete intersection, with f = 0, of a composite adjoint curve of order m + k, consisting of the adjoint curve of order m through A + B, together with the non-adjoint curve ω = 0; and the set B + B₀ consists of p points, and lies on i + j adjoint φ-curves of f = 0.",
          "type": "quote"
        },
        {
          "ref": "1963, Julian Lowell Coolidge, A History of Geometrical Methods, page 205:",
          "text": "As we have stated before, a curve f' is adjoint to a curve f if it have at least the multiplicity r#95;i-1 at each point where f has the multiplicity r#95;i. A first polar #92;sum#95;iy#95;i#92;left(#92;partialf#47;#92;partialx#95;i#92;right)#61;0 is an example of an adjoint curve.",
          "type": "quote"
        },
        {
          "ref": "2016, Eugene Wachspress, Rational Bases and Generalized Barycentrics: Applications to Finite Elements and Graphics, page 216:",
          "text": "This imposes n(n - 3)/2 conditions on the n-gon adjoint curve.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with."
      ],
      "id": "en-adjoint-en-adj-D8FiKQ1E",
      "links": [
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          "geometry"
        ],
        [
          "adjoint curve",
          "adjoint curve"
        ],
        [
          "multiple point",
          "multiple point"
        ]
      ],
      "raw_glosses": [
        "(geometry, of one curve to another curve) Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with."
      ],
      "raw_tags": [
        "of one curve to another curve"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
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    {
      "ipa": "/ˈæd͡ʒ.ɔɪnt/"
    },
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  ],
  "synonyms": [
    {
      "_dis1": "0 0 0",
      "english": "in certain contexts",
      "topics": [
        "mathematics",
        "sciences"
      ],
      "word": "adjunct"
    }
  ],
  "translations": [
    {
      "_dis1": "0 0 0",
      "code": "eo",
      "lang": "Esperanto",
      "sense": "matrix",
      "word": "adjunkta"
    },
    {
      "_dis1": "0 0 0",
      "code": "de",
      "lang": "German",
      "sense": "matrix",
      "word": "adjungiert"
    },
    {
      "_dis1": "0 0 0",
      "code": "es",
      "lang": "Spanish",
      "sense": "matrix",
      "tags": [
        "feminine"
      ],
      "word": "adjunta"
    }
  ],
  "wikipedia": [
    "Adjoint representation",
    "Adjoint representation of a Lie algebra",
    "adjoint"
  ],
  "word": "adjoint"
}

{
  "derived": [
    {
      "_dis1": "0 0 0 0 0 0 0",
      "word": "biadjoint"
    },
    {
      "_dis1": "0 0 0 0 0 0 0",
      "word": "sub-adjoint"
    }
  ],
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        "4": "",
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      "expansion": "French adjoindre (“to join”)",
      "name": "der"
    },
    {
      "args": {
        "1": "en",
        "2": "adjunct"
      },
      "expansion": "Doublet of adjunct",
      "name": "doublet"
    }
  ],
  "etymology_text": "From French adjoindre (“to join”), from late 19th C; see also adjoin. Doublet of adjunct.\nIn the case of category theory (which brings together concepts from numerous fields), the term is often confounded with adjunct and the relationship is called an adjunction. The origin of any particular usage may therefore be uncertain.",
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    {
      "form": "adjoints",
      "tags": [
        "plural"
      ]
    }
  ],
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      "args": {},
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  "lang_code": "en",
  "pos": "noun",
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      ],
      "glosses": [
        "The transpose of the cofactor matrix of a given square matrix."
      ],
      "id": "en-adjoint-en-noun-4DbFhGKe",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "transpose",
          "transpose"
        ],
        [
          "cofactor matrix",
          "cofactor matrix"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The transpose of the cofactor matrix of a given square matrix."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "100 0 0 0 0 0 0",
          "code": "de",
          "lang": "German",
          "sense": "matrix",
          "tags": [
            "feminine"
          ],
          "word": "Adjungierte"
        },
        {
          "_dis1": "100 0 0 0 0 0 0",
          "code": "es",
          "lang": "Spanish",
          "sense": "matrix",
          "tags": [
            "feminine"
          ],
          "word": "matriz de adjuntos"
        },
        {
          "_dis1": "100 0 0 0 0 0 0",
          "code": "es",
          "lang": "Spanish",
          "sense": "matrix",
          "tags": [
            "feminine"
          ],
          "word": "matriz de cofactores"
        }
      ]
    },
    {
      "categories": [
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          "kind": "topical",
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          "name": "Linear algebra",
          "orig": "en:Linear algebra",
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      "glosses": [
        "Transpose conjugate."
      ],
      "id": "en-adjoint-en-noun-r5VJhHiv",
      "links": [
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          "mathematics",
          "mathematics"
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          "matrix",
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        ],
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          "Transpose conjugate",
          "transpose conjugate"
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      "raw_glosses": [
        "(mathematics, linear algebra, of a matrix) Transpose conjugate."
      ],
      "raw_tags": [
        "of a matrix"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
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      "categories": [
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          "kind": "topical",
          "langcode": "en",
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      "glosses": [
        "Hermitian conjugate."
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          "Hermitian conjugate",
          "Hermitian conjugate"
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      "raw_glosses": [
        "(mathematics, mathematical analysis, of an operator) Hermitian conjugate."
      ],
      "raw_tags": [
        "of an operator"
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      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
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    {
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          "kind": "topical",
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          "name": "Category theory",
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        "(mathematics, category theory) A functor related to another functor by an adjunction."
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      "glosses": [
        "A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used."
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        [
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          "multiple point",
          "multiple point"
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          "sub-adjoint",
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        "(geometry, algebraic geometry) A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used."
      ],
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          "ref": "1798, Theobald Wolfe Tone, The Writings of Theobald Wolfe Tone 1763-98, Volume 3:",
          "text": ". Nominated the citizens Fayolles, captain of infantry, and Favery of the Engineers to be my adjoints, and dispatched the letters of nomination to the Minister at War, so now I am fairly afloat.",
          "type": "quote"
        },
        {
          "ref": "1884, William Morris, Art and Socialism:",
          "text": "Even as it is, by the reckless aggregation of machine-workers and their adjoints in the great cities and the manufacturing districts, it has kept down life amongst us, and keeps it down to a miserably low standard; so low that any standpoint for improvement is hard to think of even.",
          "type": "quote"
        },
        {
          "ref": "1975, Elizabeth L. Saxe, Sidney Wilfred Mintz, Working Papers in Haitian Society and Culture, page 60:",
          "text": "The chef and his adjoints are seen by this code as part of the military, subject to military jurisdiction despite their obligation to execute the orders of the administrative council and of the justice of the peace.",
          "type": "quote"
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        "An assistant to someone who holds a position in the military or civil service."
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          "ref": "1929, Chester Collins Maxey, Urban Democracy, page 89:",
          "text": "A vigorous, aggressive, and ambitious mayor will not rely overmuch upon his adjoints, but a mayor of the more passive type will lean heavily upon them.",
          "type": "quote"
        },
        {
          "ref": "1989, Alan Forrest, Conscripts and Deserters, →ISBN:",
          "text": "Mayors and their adjoints were often simple cultivateurs like the majority of the community.",
          "type": "quote"
        }
      ],
      "glosses": [
        "An assistant mayor of a French commune."
      ],
      "id": "en-adjoint-en-noun-Q4u9v2AR",
      "links": [
        [
          "assistant",
          "assistant"
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        [
          "mayor",
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        [
          "commune",
          "commune"
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  "wikipedia": [
    "adjoint"
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}

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  "categories": [
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    "Terms with German translations",
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      "word": "adjointable"
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    {
      "word": "adjoint action"
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    {
      "word": "adjoint curve"
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      "word": "adjoint endomorphism"
    },
    {
      "word": "adjoint functor"
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    {
      "word": "adjointly"
    },
    {
      "word": "adjoint matrix"
    },
    {
      "word": "adjointness"
    },
    {
      "word": "adjoint operator"
    },
    {
      "word": "adjoint representation"
    },
    {
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      "word": "nonadjoint"
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    {
      "word": "right adjoint functor"
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  "etymology_templates": [
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        "1": "en",
        "2": "adjunct"
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      "expansion": "Doublet of adjunct",
      "name": "doublet"
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  "etymology_text": "From French adjoindre (“to join”), from late 19th C; see also adjoin. Doublet of adjunct.\nIn the case of category theory (which brings together concepts from numerous fields), the term is often confounded with adjunct and the relationship is called an adjunction. The origin of any particular usage may therefore be uncertain.",
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      "tags": [
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      "word": "self-adjoint"
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        ]
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        "(mathematics) Used in certain contexts, in each case involving a pair of transformations, one of which is, or is analogous to, conjugation (either inner automorphism or complex conjugation)."
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      ]
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        "en:Mathematics"
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          "ref": "1933, H. F. Baker, Principles of Geometry, volume 5, published 2010, page 103:",
          "text": "The sets A + A₀, B + B₀, together, form the complete intersection, with f = 0, of a composite adjoint curve of order m + k, consisting of the adjoint curve of order m through A + B, together with the non-adjoint curve ω = 0; and the set B + B₀ consists of p points, and lies on i + j adjoint φ-curves of f = 0.",
          "type": "quote"
        },
        {
          "ref": "1963, Julian Lowell Coolidge, A History of Geometrical Methods, page 205:",
          "text": "As we have stated before, a curve f' is adjoint to a curve f if it have at least the multiplicity r#95;i-1 at each point where f has the multiplicity r#95;i. A first polar #92;sum#95;iy#95;i#92;left(#92;partialf#47;#92;partialx#95;i#92;right)#61;0 is an example of an adjoint curve.",
          "type": "quote"
        },
        {
          "ref": "2016, Eugene Wachspress, Rational Bases and Generalized Barycentrics: Applications to Finite Elements and Graphics, page 216:",
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          "type": "quote"
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        "Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with."
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        "(geometry, of one curve to another curve) Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with."
      ],
      "raw_tags": [
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      ],
      "tags": [
        "not-comparable"
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        "geometry",
        "mathematics",
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      "word": "adjunct"
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  "translations": [
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      "sense": "matrix",
      "word": "adjunkta"
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      "code": "de",
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    }
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    "Adjoint representation of a Lie algebra",
    "adjoint"
  ],
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}

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        "sciences"
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        "Hermitian conjugate."
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        "mathematics",
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      ],
      "topics": [
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        "geometry",
        "mathematics",
        "sciences"
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          "ref": "1798, Theobald Wolfe Tone, The Writings of Theobald Wolfe Tone 1763-98, Volume 3:",
          "text": ". Nominated the citizens Fayolles, captain of infantry, and Favery of the Engineers to be my adjoints, and dispatched the letters of nomination to the Minister at War, so now I am fairly afloat.",
          "type": "quote"
        },
        {
          "ref": "1884, William Morris, Art and Socialism:",
          "text": "Even as it is, by the reckless aggregation of machine-workers and their adjoints in the great cities and the manufacturing districts, it has kept down life amongst us, and keeps it down to a miserably low standard; so low that any standpoint for improvement is hard to think of even.",
          "type": "quote"
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        {
          "ref": "1975, Elizabeth L. Saxe, Sidney Wilfred Mintz, Working Papers in Haitian Society and Culture, page 60:",
          "text": "The chef and his adjoints are seen by this code as part of the military, subject to military jurisdiction despite their obligation to execute the orders of the administrative council and of the justice of the peace.",
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      "glosses": [
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      "links": [
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          "ref": "1929, Chester Collins Maxey, Urban Democracy, page 89:",
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          "type": "quote"
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          "ref": "1989, Alan Forrest, Conscripts and Deserters, →ISBN:",
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          "type": "quote"
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      "glosses": [
        "An assistant mayor of a French commune."
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      "code": "de",
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      "tags": [
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}