"diagonalize" meaning in All languages combined

{
  "derived": [
    {
      "_dis1": "0 0",
      "word": "diagonalizable"
    },
    {
      "_dis1": "0 0",
      "word": "diagonalization"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "diagonal",
        "3": "-ize"
      },
      "expansion": "diagonal + -ize",
      "name": "af"
    }
  ],
  "etymology_text": "From diagonal + -ize.",
  "forms": [
    {
      "form": "diagonalizes",
      "tags": [
        "present",
        "singular",
        "third-person"
      ]
    },
    {
      "form": "diagonalizing",
      "tags": [
        "participle",
        "present"
      ]
    },
    {
      "form": "diagonalized",
      "tags": [
        "participle",
        "past"
      ]
    },
    {
      "form": "diagonalized",
      "tags": [
        "past"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "diagonalize (third-person singular simple present diagonalizes, present participle diagonalizing, simple past and past participle diagonalized)",
      "name": "en-verb"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "verb",
  "related": [
    {
      "_dis1": "0 0",
      "word": "diagonalizer"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "74 26",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "69 31",
          "kind": "other",
          "name": "English terms suffixed with -ize",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse."
      ],
      "id": "en-diagonalize-en-verb-6AxjY6FW",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "square matrix",
          "square matrix"
        ],
        [
          "diagonal matrix",
          "diagonal matrix"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "inverse",
          "inverse"
        ]
      ],
      "raw_glosses": [
        "(mathematics, transitive) To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse."
      ],
      "tags": [
        "transitive"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "95 5",
          "code": "nl",
          "lang": "Dutch",
          "sense": "convert square matrix into diagonal matrix",
          "word": "diagonaliseren"
        }
      ]
    },
    {
      "categories": [],
      "examples": [
        {
          "ref": "2017, Andrew Pickering, “Ross Ashby”, in The Cybernetic Brain, University of Chicago Press, published 2010, page 159",
          "text": "And what we should do, therefore, is to diagonalize the variables—we should find some new design variables such that design problems only bear upon subsets of them that are loosely coupled to others, like the subsystems of ten lights in the example.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "To design variables such that design problems only bear upon subsets that are loosely coupled to others."
      ],
      "id": "en-diagonalize-en-verb-djet5A~m",
      "links": [
        [
          "cybernetics",
          "cybernetics"
        ],
        [
          "design",
          "design"
        ]
      ],
      "qualifier": "cybernetics",
      "raw_glosses": [
        "(cybernetics) To design variables such that design problems only bear upon subsets that are loosely coupled to others."
      ]
    }
  ],
  "synonyms": [
    {
      "_dis1": "0 0",
      "english": "non-Oxford British English",
      "word": "diagonalise"
    }
  ],
  "word": "diagonalize"
}

{
  "categories": [
    "English entries with incorrect language header",
    "English lemmas",
    "English terms suffixed with -ize",
    "English verbs"
  ],
  "derived": [
    {
      "word": "diagonalizable"
    },
    {
      "word": "diagonalization"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "diagonal",
        "3": "-ize"
      },
      "expansion": "diagonal + -ize",
      "name": "af"
    }
  ],
  "etymology_text": "From diagonal + -ize.",
  "forms": [
    {
      "form": "diagonalizes",
      "tags": [
        "present",
        "singular",
        "third-person"
      ]
    },
    {
      "form": "diagonalizing",
      "tags": [
        "participle",
        "present"
      ]
    },
    {
      "form": "diagonalized",
      "tags": [
        "participle",
        "past"
      ]
    },
    {
      "form": "diagonalized",
      "tags": [
        "past"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "diagonalize (third-person singular simple present diagonalizes, present participle diagonalizing, simple past and past participle diagonalized)",
      "name": "en-verb"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "verb",
  "related": [
    {
      "word": "diagonalizer"
    }
  ],
  "senses": [
    {
      "categories": [
        "English transitive verbs",
        "en:Mathematics"
      ],
      "glosses": [
        "To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "square matrix",
          "square matrix"
        ],
        [
          "diagonal matrix",
          "diagonal matrix"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "inverse",
          "inverse"
        ]
      ],
      "raw_glosses": [
        "(mathematics, transitive) To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse."
      ],
      "tags": [
        "transitive"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "English terms with quotations"
      ],
      "examples": [
        {
          "ref": "2017, Andrew Pickering, “Ross Ashby”, in The Cybernetic Brain, University of Chicago Press, published 2010, page 159",
          "text": "And what we should do, therefore, is to diagonalize the variables—we should find some new design variables such that design problems only bear upon subsets of them that are loosely coupled to others, like the subsystems of ten lights in the example.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "To design variables such that design problems only bear upon subsets that are loosely coupled to others."
      ],
      "links": [
        [
          "cybernetics",
          "cybernetics"
        ],
        [
          "design",
          "design"
        ]
      ],
      "qualifier": "cybernetics",
      "raw_glosses": [
        "(cybernetics) To design variables such that design problems only bear upon subsets that are loosely coupled to others."
      ]
    }
  ],
  "synonyms": [
    {
      "english": "non-Oxford British English",
      "word": "diagonalise"
    }
  ],
  "translations": [
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "convert square matrix into diagonal matrix",
      "word": "diagonaliseren"
    }
  ],
  "word": "diagonalize"
}