See determinant in All languages combined, or Wiktionary
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Deif, Advanced Matrix Theory for Scientists and Engineers, Gordon and Breach Science Publishers (Abacus Press), 2nd Edition, page 18,\nShow that the determinant of a Hermitian matrix is real and that of a skew-Hermitian matrix is imaginary." }, { "ref": "2009, Richard A. Brualdi, Dragoš Cvetkoviċ, A Combinatorial Approach to Matrix Theory and Its Applications, Taylor & Francis (CRC / Chapman & Hall), page 63:", "text": "Using this definition, we derive the basic properties of a determinant that are useful in its evaluation. In particular, it is shown how the calculation of a determinant can be reduced to the calculation of determinants of lower order.", "type": "quote" } ], "glosses": [ "A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value 1 for the unit matrix; abbreviated as: det." ], "id": "en-determinant-en-noun-1WUiSn-~", "links": [ [ "linear algebra", "linear algebra" ], [ "scalar", "scalar" ], [ "transformation matrix", "transformation matrix" ], [ "matrices", "matrix" ], [ "distributive", "distributive" ], [ "multilinear", "multilinear" ], [ "unit matrix", "unit matrix" ], [ "det", "det" ] ], "raw_glosses": [ "(linear algebra) A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in 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certain characteristics of a square matrix", "tags": [ "common-gender" ], "word": "determinant" }, { "_dis1": "2 86 7 5", "code": "nl", "lang": "Dutch", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinant" }, { "_dis1": "2 86 7 5", "code": "et", "lang": "Estonian", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determinant" }, { "_dis1": "2 86 7 5", "code": "fi", "lang": "Finnish", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determinantti" }, { "_dis1": "2 86 7 5", "code": "fr", "lang": "French", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "déterminant" }, { "_dis1": "2 86 7 5", "code": "de", "lang": "German", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "feminine" ], "word": "Determinante" }, { "_dis1": "2 86 7 5", "code": "el", "lang": "Greek", "roman": "orízousa", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "feminine" ], "word": "ορίζουσα" }, { "_dis1": "2 86 7 5", "code": "hu", "lang": "Hungarian", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determináns" }, { "_dis1": "2 86 7 5", "code": "is", "lang": "Icelandic", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "feminine" ], "word": "ákveða" }, { "_dis1": "2 86 7 5", "code": "id", "lang": "Indonesian", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determinan" }, { "_dis1": "2 86 7 5", "code": "it", "lang": "Italian", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinante" }, { "_dis1": "2 86 7 5", "code": "ja", "lang": "Japanese", "roman": "gyōretsu-shiki", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "行列式" }, { "_dis1": "2 86 7 5", "alt": "行列式", "code": "ko", "lang": "Korean", "roman": "haengnyeolsik", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "행렬식" }, { "_dis1": "2 86 7 5", "code": "ms", "lang": "Malay", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "penentu" }, { "_dis1": "2 86 7 5", "code": "no", "lang": "Norwegian", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinant" }, { "_dis1": "2 86 7 5", "code": "pl", "lang": "Polish", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "wyznacznik" }, { "_dis1": "2 86 7 5", "code": "pt", "lang": "Portuguese", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinante" }, { "_dis1": "2 86 7 5", "code": "ru", "lang": "Russian", "roman": "determinánt", "sense": "scalar that encodes 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In particular, it is shown how the calculation of a determinant can be reduced to the calculation of determinants of lower order.", "type": "quote" } ], "glosses": [ "A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value 1 for the unit matrix; abbreviated as: det." ], "links": [ [ "linear algebra", "linear algebra" ], [ "scalar", "scalar" ], [ "transformation matrix", "transformation matrix" ], [ "matrices", "matrix" ], [ "distributive", "distributive" ], [ "multilinear", "multilinear" ], [ "unit matrix", "unit matrix" ], [ "det", "det" ] ], "raw_glosses": [ "(linear algebra) A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value 1 for the unit matrix; abbreviated as: det." ], "topics": [ "linear-algebra", "mathematics", "sciences" ] }, { "categories": [ "en:Biology" ], "glosses": [ "A substance that causes a cell to adopt a particular fate." ], "links": [ [ "biology", "biology" ], [ "cell", "cell" ] ], "raw_glosses": [ "(biology) A substance that causes a cell to adopt a particular fate." ], "topics": [ "biology", "natural-sciences" ] }, { "categories": [ "en:Genetics" ], "glosses": [ "Something that causes a nuclease to cut at a specified point" ], "links": [ [ "genetics", "genetics" ], [ "nuclease", "nuclease" ], [ "cut", "cut" ] ], "raw_glosses": [ "(genetics) Something that causes a nuclease to cut at a specified point" ], "topics": [ "biology", "genetics", "medicine", "natural-sciences", "sciences" ] } ], "sounds": [ { "ipa": "/dɪˈtɜːmɪnənt/", "tags": [ "General-Australian", "UK" ] }, { "ipa": "/dɪˈtɝmɪnənt/", "tags": [ "Canada", "General-American" ] }, { "ipa": "/dɪˈtɝmənənt/", "tags": [ "Canada", "General-American" ] } ], "translations": [ { "code": "ar", "lang": "Arabic", "roman": "muḥaddidun", "sense": "determining factor", "tags": [ "masculine" ], "word": "مُحَدِّدٌ" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "determining factor", "word": "決定(性)因素" }, { "alt": "juédìng(xìng) yīnsù", "code": "cmn", "lang": "Chinese Mandarin", "sense": "determining factor", "word": "决定(性)因素" }, { "code": "fi", "lang": "Finnish", "sense": "determining factor", "word": "määräävä tekijä" }, { "code": "fi", "lang": "Finnish", "sense": "determining factor", "word": "ratkaiseva tekijä" }, { "code": "fr", "lang": "French", "sense": "determining factor", "tags": [ "masculine" ], "word": "déterminant" }, { "code": "hu", "lang": "Hungarian", "sense": "determining factor", "word": "meghatározó" }, { "code": "id", "lang": "Indonesian", "sense": "determining factor", "word": "determinan" }, { "code": "id", "lang": "Indonesian", "sense": "determining factor", "word": "penentu" }, { "code": "ga", "lang": "Irish", "sense": "determining factor", "tags": [ "masculine" ], "word": "cinntitheach" }, { "code": "no", "lang": "Norwegian", "sense": "determining factor", "tags": [ "masculine" ], "word": "determinant" }, { "code": "pt", "lang": "Portuguese", "sense": "determining factor", "tags": [ "masculine" ], "word": "determinante" }, { "code": "ru", "lang": "Russian", "roman": "opredeljájuščij fáktor", "sense": "determining factor", "tags": [ "masculine" ], "word": "определя́ющий фа́ктор" }, { "code": "ru", "lang": "Russian", "roman": "opredelítelʹ", "sense": "determining factor", "tags": [ "masculine" ], "word": "определи́тель" }, { "code": "bg", "lang": "Bulgarian", "roman": "determinanta", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "feminine" ], "word": "детерминанта" }, { "code": "ca", "lang": "Catalan", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinant" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "hánglièshì", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "行列式" }, { "code": "cs", "lang": "Czech", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinant" }, { "code": "da", "lang": "Danish", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "common-gender" ], "word": "determinant" }, { "code": "nl", "lang": "Dutch", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinant" }, { "code": "et", "lang": "Estonian", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determinant" }, { "code": "fi", "lang": "Finnish", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determinantti" }, { "code": "fr", "lang": "French", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "déterminant" }, { "code": "de", "lang": "German", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "feminine" ], "word": "Determinante" }, { "code": "el", "lang": "Greek", "roman": "orízousa", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "feminine" ], "word": "ορίζουσα" }, { "code": "hu", "lang": "Hungarian", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determináns" }, { "code": "is", "lang": "Icelandic", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "feminine" ], "word": "ákveða" }, { "code": "id", "lang": "Indonesian", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "determinan" }, { "code": "it", "lang": "Italian", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinante" }, { "code": "ja", "lang": "Japanese", "roman": "gyōretsu-shiki", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "行列式" }, { "alt": "行列式", "code": "ko", "lang": "Korean", "roman": "haengnyeolsik", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "행렬식" }, { "code": "ms", "lang": "Malay", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "penentu" }, { "code": "no", "lang": "Norwegian", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinant" }, { "code": "pl", "lang": "Polish", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "wyznacznik" }, { "code": "pt", "lang": "Portuguese", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinante" }, { "code": "ru", "lang": "Russian", "roman": "determinánt", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "детермина́нт" }, { "code": "sk", "lang": "Slovak", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinant" }, { "code": "es", "lang": "Spanish", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "masculine" ], "word": "determinante" }, { "code": "sv", "lang": "Swedish", "sense": "scalar that encodes certain characteristics of a square matrix", "tags": [ "common-gender" ], "word": "determinant" }, { "code": "tl", "lang": "Tagalog", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "taliyak" }, { "code": "vi", "lang": "Vietnamese", "sense": "scalar that encodes certain characteristics of a square matrix", "word": "định thức" } ], "wikipedia": [ "determinant" ], "word": "determinant" } { "categories": [ "English adjectives", "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms borrowed from French", "English terms derived from French", "Entries with translation boxes", "Pages with 10 entries", "Pages with entries", "Terms with Arabic translations", "Terms with Bulgarian translations", "Terms with Catalan translations", "Terms with Czech translations", "Terms with Danish translations", "Terms with Dutch translations", "Terms with Estonian translations", "Terms with Finnish translations", "Terms with French translations", "Terms with German translations", "Terms with Greek translations", "Terms with Hungarian translations", "Terms with Icelandic translations", "Terms with Indonesian translations", "Terms with Irish translations", "Terms with Italian translations", "Terms with Japanese translations", "Terms with Korean translations", "Terms with Malay translations", "Terms with Mandarin translations", "Terms with Norwegian translations", "Terms with Polish translations", "Terms with Portuguese translations", "Terms with Russian translations", "Terms with Slovak translations", "Terms with Spanish translations", "Terms with Swedish translations", "Terms with Tagalog translations", "Terms with Vietnamese translations" ], "derived": [ { "word": "self-determinant" } ], "etymology_templates": [ { "args": { "1": "en", "2": "fr", "3": "déterminant" }, "expansion": "French déterminant", "name": "bor" } ], "etymology_text": "Borrowed from French déterminant.", "forms": [ { "form": "more determinant", "tags": [ "comparative" ] }, { "form": "most determinant", "tags": [ "superlative" ] } ], "head_templates": [ { "args": {}, "expansion": "determinant (comparative more determinant, superlative most determinant)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "related": [ { "word": "permanent" }, { "word": "singular" } ], "senses": [ { "glosses": [ "Serving to determine or limit; determinative." ], "links": [ [ "determinative", "determinative" ] ] } ], "sounds": [ { "ipa": "/dɪˈtɜːmɪnənt/", "tags": [ "General-Australian", "UK" ] }, { "ipa": "/dɪˈtɝmɪnənt/", "tags": [ "Canada", "General-American" ] }, { "ipa": "/dɪˈtɝmənənt/", "tags": [ "Canada", "General-American" ] } ], "wikipedia": [ "determinant" ], "word": "determinant" }
Download raw JSONL data for determinant meaning in English (14.3kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.