"conjugate transpose" meaning in English

{
  "forms": [
    {
      "form": "conjugate transposes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "conjugate transpose (plural conjugate transposes)",
      "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"
        },
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          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
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        },
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          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Polish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The transpose of a matrix, after replacing each element with its complex conjugate."
      ],
      "id": "en-conjugate_transpose-en-noun-Jmjwouzy",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "transpose",
          "transpose"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "complex conjugate",
          "complex conjugate"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The transpose of a matrix, after replacing each element with its complex conjugate."
      ],
      "related": [
        {
          "english": "adjoint; historically also sometimes called",
          "word": "adjugate matrix"
        }
      ],
      "synonyms": [
        {
          "sense": "transpose of matrix of complex conjugates",
          "word": "adjoint matrix"
        },
        {
          "sense": "transpose of matrix of complex conjugates",
          "word": "bedaggered matrix"
        },
        {
          "sense": "transpose of matrix of complex conjugates",
          "word": "Hermitian conjugate"
        },
        {
          "sense": "transpose of matrix of complex conjugates",
          "word": "Hermitian transpose"
        },
        {
          "sense": "transpose of matrix of complex conjugates",
          "word": "transjugate"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "konjugierte Transponierte"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "konjugiert-transponierte Matrix"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "Hermitesch Transponierte"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "Hermitesch transponierte Matrix"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "sprzężenie hermitowskie macierzy"
        }
      ],
      "wikipedia": [
        "Conjugate transpose",
        "Moore–Penrose pseudoinverse"
      ]
    }
  ],
  "word": "conjugate transpose"
}

{
  "forms": [
    {
      "form": "conjugate transposes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "conjugate transpose (plural conjugate transposes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "english": "adjoint; historically also sometimes called",
      "word": "adjugate matrix"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with German translations",
        "Terms with Polish translations",
        "Translation table header lacks gloss",
        "en:Mathematics"
      ],
      "glosses": [
        "The transpose of a matrix, after replacing each element with its complex conjugate."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "transpose",
          "transpose"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "complex conjugate",
          "complex conjugate"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The transpose of a matrix, after replacing each element with its complex conjugate."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Conjugate transpose",
        "Moore–Penrose pseudoinverse"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "transpose of matrix of complex conjugates",
      "word": "adjoint matrix"
    },
    {
      "sense": "transpose of matrix of complex conjugates",
      "word": "bedaggered matrix"
    },
    {
      "sense": "transpose of matrix of complex conjugates",
      "word": "Hermitian conjugate"
    },
    {
      "sense": "transpose of matrix of complex conjugates",
      "word": "Hermitian transpose"
    },
    {
      "sense": "transpose of matrix of complex conjugates",
      "word": "transjugate"
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "konjugierte Transponierte"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "konjugiert-transponierte Matrix"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "Hermitesch Transponierte"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "Hermitesch transponierte Matrix"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "sprzężenie hermitowskie macierzy"
    }
  ],
  "word": "conjugate transpose"
}