"semiorthogonal" meaning in All languages combined

See semiorthogonal on Wiktionary

Adjective [English]

Etymology: From semi- + orthogonal. Etymology templates: {{prefix|en|semi|orthogonal}} semi- + orthogonal Head templates: {{en-adj|-}} semiorthogonal (not comparable)
  1. (mathematics, category theory) Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory. Tags: not-comparable Categories (topical): Category theory, Mathematics
    Sense id: en-semiorthogonal-en-adj-eH9GxGGO Categories (other): English entries with incorrect language header, English terms prefixed with semi-, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 36 36 28 Disambiguation of English terms prefixed with semi-: 34 40 26 Disambiguation of Pages with 1 entry: 34 40 27 Disambiguation of Pages with entries: 32 38 29 Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences
  2. (mathematics, matrix algebra) Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix). Tags: not-comparable Categories (topical): Mathematics
    Sense id: en-semiorthogonal-en-adj-rHMJV182 Categories (other): English entries with incorrect language header, English terms prefixed with semi-, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 36 36 28 Disambiguation of English terms prefixed with semi-: 34 40 26 Disambiguation of Pages with 1 entry: 34 40 27 Disambiguation of Pages with entries: 32 38 29 Topics: mathematics, sciences
  3. (physics) Orthogonal to the corresponding approximation space. Tags: not-comparable Categories (topical): Physics
    Sense id: en-semiorthogonal-en-adj-dzX-V6cO Categories (other): English entries with incorrect language header, English terms prefixed with semi-, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 36 36 28 Disambiguation of English terms prefixed with semi-: 34 40 26 Disambiguation of Pages with 1 entry: 34 40 27 Disambiguation of Pages with entries: 32 38 29 Topics: natural-sciences, physical-sciences, physics
{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "semi",
        "3": "orthogonal"
      },
      "expansion": "semi- + orthogonal",
      "name": "prefix"
    }
  ],
  "etymology_text": "From semi- + orthogonal.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "semiorthogonal (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "36 36 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "34 40 26",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "34 40 27",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "32 38 29",
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "ref": "2015, Asher Auel, Marcello Bernardara, “Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields”, in arXiv:",
          "text": "For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles..",
          "type": "quote"
        }
      ],
      "glosses": [
        "Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory."
      ],
      "id": "en-semiorthogonal-en-adj-eH9GxGGO",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "category theory",
          "category theory"
        ]
      ],
      "raw_glosses": [
        "(mathematics, category theory) Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "36 36 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "34 40 26",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "34 40 27",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "32 38 29",
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix)."
      ],
      "id": "en-semiorthogonal-en-adj-rHMJV182",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "columnwise",
          "columnwise"
        ],
        [
          "orthogonal",
          "orthogonal"
        ],
        [
          "rowwise",
          "rowwise"
        ]
      ],
      "qualifier": "matrix algebra",
      "raw_glosses": [
        "(mathematics, matrix algebra) Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix)."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Physics",
          "orig": "en:Physics",
          "parents": [
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "36 36 28",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "34 40 26",
          "kind": "other",
          "name": "English terms prefixed with semi-",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "34 40 27",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "32 38 29",
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "Orthogonal to the corresponding approximation space."
      ],
      "id": "en-semiorthogonal-en-adj-dzX-V6cO",
      "links": [
        [
          "physics",
          "physics"
        ]
      ],
      "raw_glosses": [
        "(physics) Orthogonal to the corresponding approximation space."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "natural-sciences",
        "physical-sciences",
        "physics"
      ]
    }
  ],
  "word": "semiorthogonal"
}
{
  "categories": [
    "English adjectives",
    "English entries with incorrect language header",
    "English lemmas",
    "English terms prefixed with semi-",
    "English uncomparable adjectives",
    "Pages with 1 entry",
    "Pages with entries"
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "semi",
        "3": "orthogonal"
      },
      "expansion": "semi- + orthogonal",
      "name": "prefix"
    }
  ],
  "etymology_text": "From semi- + orthogonal.",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "semiorthogonal (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Category theory",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2015, Asher Auel, Marcello Bernardara, “Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields”, in arXiv:",
          "text": "For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles..",
          "type": "quote"
        }
      ],
      "glosses": [
        "Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "category theory",
          "category theory"
        ]
      ],
      "raw_glosses": [
        "(mathematics, category theory) Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "columnwise",
          "columnwise"
        ],
        [
          "orthogonal",
          "orthogonal"
        ],
        [
          "rowwise",
          "rowwise"
        ]
      ],
      "qualifier": "matrix algebra",
      "raw_glosses": [
        "(mathematics, matrix algebra) Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix)."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Physics"
      ],
      "glosses": [
        "Orthogonal to the corresponding approximation space."
      ],
      "links": [
        [
          "physics",
          "physics"
        ]
      ],
      "raw_glosses": [
        "(physics) Orthogonal to the corresponding approximation space."
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "natural-sciences",
        "physical-sciences",
        "physics"
      ]
    }
  ],
  "word": "semiorthogonal"
}

Download raw JSONL data for semiorthogonal meaning in All languages combined (2.7kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-03-01 from the enwiktionary dump dated 2025-02-21 using wiktextract (7c21d10 and f2e72e5). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.