Difference between revisions of "Language/Multiple-languages/Vocabulary/Algebra"

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[[Category:Sci-Tech_Index]]
{{Sci-Tech-Index-Intro}}
This is a part of the Sci-Tech Index, a project for science and technology learners.


You can see the titles are a bit of weird. They are going to be read by machine and made use of by other means.
{| class="wikitable sortable"
! cmn-Hans-CN: 科目
! cmn-Latn.Pinyin-CN: kēmù
! deu-Latn-DE: Fach [n]
! eng-Latn-US: subject
! fra-Latn-FR: matière [f]
! jpn-Jpan-JP: 科目
! jpn-Hrkt-JP: か↑もく
! rus-Cyrl-RU: предме́т
|-
|
|
|
|
|
|
|
|
|-
| 抽象代数
| chōuxiàng dàishù
| abstrakte Algebra
| abstract algebra
| algèbre générale, algèbre abstraite
| 抽象代数学
| ちゅ↑うしょうだいす↓うがく
| абстра́ктная а́лгебра, общая а́лгебра, вы́сшая а́лгебра
|-
| 群论
| qún lùn
| Gruppentheorie [f]
| group theory
| théorie [f] des groupes [m pl]
| 群論
| ぐ↓んろん
| тео́рия групп
|-
| 环论
| huán lùn
| Ringtheorie [f]
| ring theory
| théorie [f] des anneaux [m pl]
| 環論
| か↑んろん
| тео́рия коле́ц
|-
| 范畴论
| fànchóu lùn
| Kategorientheorie [f]
| category theory
| théorie [f] des catégories [f pl]
| 圏論
| け↑んろん
| тео́рия катего́рий
|-
| 交换代数
| jiāohuàn dàishù
| kommutative Algebra
| commutative algebra
| algèbre [f] commutative
| 可換環論
| か↑かんか↓んろん
| коммутати́вная а́лгебра
|-
| 线性代数
| xiànxìng dàishù
| lineare Algebra, Vektoralgebra [f]
| linear algebra
| algèbre [f] linéaire
| 線型代数
| せ↑んけいだいす↓うがく
| лине́йная а́лгебра
|-
| 多重线性代数
| duōchóng xiànxìng dàishù
| multilineare Algebra
| multilinear algebra
| algèbre [f] multilinéaire
| 多重線型代数
| た↑じゅうせんけいだいす↓う
| полилине́йная а́лгебра
|-
| 泛代数
| fàn dàishù
| universelle Algebra, allgemeine Algebra
| universal algebra, common algebra
| algèbre [f] universelle
| 普遍代数学，一般代数学
| ふ↑へんだいすう↓がく，い↑っぱんだいすう↓がく
| универса́льная а́лгебра
|-
| 同调代数
| tóngdiào dàishù
| homologische Algebra
| homological algebra
| algèbre [f] homologique
| ホモロジー代数学
| ホ↑モロジ↓ーだいす↑うがく
| гомологи́ческая а́лгебра
|-
|
|
|
|
|
|
|
|
|}


“Prerequisites” for non-English languages are to be generated through programs, so they are kept empty.
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
| 代数方程 ||
| dàishù fāngchéng ||
| algebraische Gleichung ||
| algebraic equation || coefficient
| équation polynomiale, équation [f] algébrique ||
| 代数方程式 ||
| だ↑いす↓うほ↑うて↓いしき ||
| алгебраи́ческое уравне́ние ||
|-
| 代数式 ||
| dàishù shì ||
| algebraischer Ausdruck ||
| algebraic expression || expression <mathematical logic>; integer; constant; variable; algebraic operation
| expression [f] algébrique ||
| 代数式 ||
| だ↑いす↓うしき ||
| алгебраи́ческим выраже́нием ||
|-
| 代数分式 ||
| dàishù fēnshì ||
|  ||
| algebraic fraction || fraction; algebraic expression
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| algebraic operation || operation <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
| 最大值自变量点集 ||
| zuìdàzhí zìbiànliàng diǎn jí ||
| Argument [n] des Maximums [n] ||
| argument of the maximum || domain <mathematical logic>; maximum <mathematical analysis>
| argument [m] du maximum [m] ||
| 最大点作用素集合 ||
| さ↑いだいてんさ↓ようそしゅうごう ||
| аргуме́нт максимиза́ции ||
|-
| 最小值自变量点集 ||
| zuìxiǎozhí zìbiànliàng diǎn jí ||
| Argument [n] des Minimums [n] ||
| argument of the minimum || domain <mathematical logic>; minimum <mathematical analysis>
| argument [m] du minimum [m] ||
| 最小点作用素集合 ||
| さ↑いしょうてんさ↓ようそしゅうごう ||
| аргуме́нт минимиза́ции ||
|-
| 二项式 ||
| èrxiàng shì ||
| Binom [n] ||
| binomial ||
| binôme [m] ||
| 二項式 ||
| に↑こうしき ||
| бино́м, двучле́н ||
|-
| 系数 ||
| xì shù ||
| Koeffizient [n], Beizahl [f], Vorzahl [f] ||
| coefficient || multiplication <number theory>; expression <mathematical logic>
| coefficient [f] ||
| 係数 ||
| け↑いす↓う ||
| коэффицие́нт ||
|-
| 常数函数 ||
| chángshù hánshù ||
| konstante Funktion ||
| constant function || constant <number theory>; function
| fonction constante ||
| 定数関数 ||
| て↑いすうか↓んすう ||
| конста́нтная фу́нкция, постоя́нная фу́нкция ||
|-
|  ||
|  ||
|  ||
| constant term || term <logic>; algebraic expression; constant
|  ||
|  ||
|  ||
|  ||
|-
| 因变量 ||
| yīn biànliàng ||
| abhängige Variable ||
| dependent variable || fraction; operand <mathematical logic>
| variable dépendante ||
| 従属変数 ||
| じ↑ゅうぞくへ↓んすう ||
| зави́симая переме́нная ||
|-
| 等式，方程 ||
| děng shì, fāngchéng ||
| Gleichung [f] ||
| equation || equality <mathematical logic>; expression <mathematical logic>
| équation [f] ||
|  ||
|  ||
|  ||
|-
| 偶函数 ||
| ǒu hánshù ||
| gerade Funktion ||
| even function || function <mathematical logic>; line symmetry <geometry>
| fonction paire ||
| 偶関数 ||
| ぐ↑うかんす↓う ||
| чётная фу́нкция ||
|-
|  ||
|  ||
|  ||
| identity || equality <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
| 单位元，中立元 ||
| dānwèi yuán, zhōnglì yuán ||
| neutrales Element ||
| identity element, neutral element || set <mathematical logic>; binary operation <mathematical logic>
| élément [m] neutre, élément [m] identité ||
| 単位元，中立元 ||
| た↑んいげん，ちゅ↑うりつげん ||
| нейтра́льный элеме́нт ||
|-
| 自变量 ||
| zì biànliàng ||
| unabhängige Variable ||
| independent variable || function <mathematical logic>
| variable indépendante ||
| 独立変数 ||
| ど↑くりつへ↓んすう ||
| незави́симая переме́нная ||
|-
| 未定元 ||
| wèidìng yuán ||
| Unbestimmte [f] ||
| indeterminate || variable
| indéterminée [f] ||
| 不定元 ||
| ふ↑ていげん ||
| неопределённый ||
|-
| 不等式 ||
| bùděng shì ||
| Ungleichung [f] ||
| inequation || inequality <mathematical logic>
| inéquation [f] ||
| 不等式 ||
| ふ↑と↓うしき ||
| неуравне́ние ||
|-
| 代数分式  ||
| dàishù fēnshì ||
|  ||
| irrational fraction || algebraic fraction; polynomial; exponent
|  ||
|  ||
|  ||
|  ||
|-
| 不可约多项式 ||
| bùkěyuē duōxiàngshì ||
| irreduzibles Polynom ||
| irreducible polynomial || polynomial; factorization
| polynôme [m] irréductible ||
| 既約多項式 ||
| き↑やくたこ↓うしき ||
| неприводимый многочле́н ||
|-
| 一次方程 ||
| yīcì fāngchéng ||
| lineare Gleichung ||
| linear equation || equation; coefficient
| équation linéaire ||
| 一次方程式 ||
| い↑ち↓じほ↑うて↓いしき ||
| лине́йное уравне́ние ||
|-
|  ||
|  ||
|  ||
| left identity || identity element <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| monomial || variable; natural number
|  ||
|  ||
|  ||
|  ||
|-
| 奇函数 ||
| jī hánshù ||
| ungerade Funktion ||
| odd function || function <mathematical logic>; point symmetry <geometry>
| fonction impaire ||
| 奇関数 ||
| き↑か↓んすう ||
| нечётная фу́нкция ||
|-
|  ||
|  ||
|  ||
| parameter ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| partial fraction decomposition, partial fraction expansion || algebraic fraction; polynomial
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| polynomial || expression <mathematical logic>; coefficient; indeterminate
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| polynomial function || polynomial; function <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| quadratic equation || equation; coefficient
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| rational function || algebraic fraction; polynomial
|  ||
|  ||
|  ||
|  ||
|-
| 可约多项式 ||
| kěyuē duōxiàngshì ||
| reduzibles Polynom ||
| reducible polynomial || polynomial; factorization
| polynôme [m] réductible ||
| 可約多項式 ||
| か↑やくたこ↓うしき ||
| приводимый многочле́н ||
|-
|  ||
|  ||
|  ||
| right identity || identity element <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| solution || equation
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| square || exponentiation <number theory>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| system of equations, simultaneous equations || finite set <mathematical logic>; equation
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| unknown || variable
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| variable || mathematical object <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| zero; root || domain; solution
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}


In progress.
== Abstract Algebra ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| algebraic structure || underlying set; arity; identity
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| arity || argument <mathematical logic>; operand <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Boolean domain || set; tautology <logic>; falsity <logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| direct product || Cartesian product <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| field || set <mathematical logic>; basic operations <number theory>; rational number <number theory>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| inverse element || set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| underlying set, carrier set || empty set <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}


{| class="wikitable"
=== Group Theory ===
!eng-Latn-US: concept
{| class="wikitable sortable"
!eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
!cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
!cmn-Hans-CN: 前提
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
!cmn-Latn.Pinyin-CN: gàiniàn
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
!cmn-Latn.Pinyin-CN: qiántí
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
!deu-Latn-DE: Begriff [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
!deu-Latn-DE: Voraussetzung [f]
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
!fra-Latn-FR: concept [m]
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
!fra-Latn-FR: préalable [m]
!jpn-Hrkt-JP: がいねん
!jpn-Hrkt-JP: ぜんたい
!jpn-Jpan-JP: 概念
!jpn-Jpan-JP: 前提
!rus-Cyrl-RU: конце́пция
!rus-Cyrl-RU: предпосы́лка
|-
|-
|abstract algebra
| ||
|
|  ||  
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|  ||  
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|  ||  
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| ||  
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| ||  
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| ||  
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| ||  
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|commutative algebra
| ||
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|  ||  
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|  ||  
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| Cayley table || finite group
|
| ||  
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| ||  
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|-
|-
|group theory
| ||
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|  ||  
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|  ||  
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| group || set <mathematical logic>
|
| ||  
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| ||  
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| ||  
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| ||  
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|-
|-
|linear algebra
| ||
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|  ||  
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|  ||  
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| finite group || underlying set; finite set <mathematical logic>
|
| ||  
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| ||  
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| ||  
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| ||  
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|-
|-
|multilinear algebra
| ||
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|  ||  
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|  ||  
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| normal subgroup, invariant subgroup || subgroup; conjugation
|
| ||  
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| ||  
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| ||  
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|-
|-
|universal algebra, common algebra
| ||
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|  ||  
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|  ||  
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| open interval || interval
|
| ||  
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| ||  
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| ||  
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| ||  
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|-
|-
|homological algebra
| ||
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|  ||
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|  ||
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| semigroup || algebraic structure; associative property
|
|  ||
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|  ||
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|  ||
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|  ||
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|-
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|  ||
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|  ||
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|  ||
|
| subgroup || group; binary operation <mathematical logic>
|
|  ||
|
|  ||
|
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
=== Ring Theory ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||  
|  ||
|  ||
| ring ||
|  ||  
|  ||  
|  ||  
|  ||  
|-
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|}
|}


== * Related Free Educational Resources ==
== Commutative Algebra ==
{| class="wikitable"
{| class="wikitable sortable"
!branch
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
!name
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
!link
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
!language
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
!public license
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
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|  ||
|  ||
|  ||
|  ||
|  ||
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|-
|-
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|  ||  
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|}
|}


[[File:640px-Quadratic_formula.svg.png]]
== Linear Algebra ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| basis || linear combination
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| characteristic equation || characteristic polynomial
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| characteristic polynomial || square matrix; eigenvalue; matrix similarity; zero
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| conjugate matrix, Hermitian matrix || conjugate transpose
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| conjugate transpose, Hermitian transpose || complex conjugate <mathematical logic>; transpose
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| diagonal matrix || matrix; main diagonal
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| identity matrix || square matrix; main diagonal
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| invertible matrix, nonsingular matrix || identity matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| linear combination || expression <mathematical logic>; coefficient; vector space
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| linear dependence || linear combination
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| linear independence || linear combination
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| linear mapping || vector addition; scalar multiplication
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| linear transformation || linear mapping
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| binary matrix, logical matrix, relation matrix, Boolean matrix || matrix; Boolean domain
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| like terms || term <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| lower triangular matrix || triangular matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| main diagonal || matrix; diagonal <geometry>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| matrix || rectangle <geometry>; expression <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| matrix addition || matrix; addition <number theory>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| matrix of ones || matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| matrix multiplication || matrix; multiplication <number theory>; addition <number theory>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| matrix similarity || invertible matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| proportional function || proportionality <number theory>; function <mathematical logic>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| rotation matrix || linear transformation; rotation <geometry>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| skew-Hermitian matrix, anti-Hermitian matrix || Hermitian matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| square matrix || matrix; square <geometry>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| system of linear equations; linear system || linear equation
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| transformation matrix || linear transformation; matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| translation matrix || translation <geometry>; matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| transpose || reflection <geometry>; main diagonal
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| triangular matrix || square matrix; triangle <geometry>
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| upper triangular matrix || triangular matrix
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
{| class="wikitable sortable"
|+ theorem in linear algebra
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
| theorem in linear algebra ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
| Cayley–Hamilton theorem || characteristic polynomial; identity matrix; determinant; scalar; ring
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
== Multilinear Algebra ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
== Universal Algebra ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
== Homological Algebra ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|-
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|  ||
|}
 
<center>
https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Quadratic_function_graph_key_values.svg/480px-Quadratic_function_graph_key_values.svg.png
</center>
 
{{Sci-Tech-Index-Menu}}


== <div style="color:#ffad00; font-weight:bold;">-- AUTHOR --</div> ==
==Other Lessons==
[https://polyglotclub.com/member/GrimPixel GrimPixel]
* [[Language/Multiple-languages/Vocabulary/Category-Theory|Category Theory]]
* [[Language/Multiple-languages/Vocabulary/Mechanics|Mechanics]]
* [[Language/Multiple-languages/Vocabulary/Animal-sounds-in-many-languages|Animal sounds in many languages]]
* [[Language/Multiple-languages/Vocabulary/Common-Han-Characters-with-⾡|Common Han Characters with ⾡]]
* [[Language/Multiple-languages/Vocabulary/Machine-Element|Machine Element]]
* [[Language/Multiple-languages/Vocabulary/Body-in-many-languages|Body in many languages]]
* [[Language/Multiple-languages/Vocabulary/Mathematical-Logic|Mathematical Logic]]
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]]
* [[Language/Multiple-languages/Vocabulary/Greetings-in-All-Languages|Greetings in All Languages]]
* [[Language/Multiple-languages/Vocabulary/Greetings-General-greeting|Greetings General greeting]]
<span links></span>

Latest revision as of 13:15, 27 March 2023

Hello polyglots, 😀

On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.

cmn-Hans-CN: 科目 cmn-Latn.Pinyin-CN: kēmù deu-Latn-DE: Fach [n] eng-Latn-US: subject fra-Latn-FR: matière [f] jpn-Jpan-JP: 科目 jpn-Hrkt-JP: か↑もく rus-Cyrl-RU: предме́т
抽象代数 chōuxiàng dàishù abstrakte Algebra abstract algebra algèbre générale, algèbre abstraite 抽象代数学 ちゅ↑うしょうだいす↓うがく абстра́ктная а́лгебра, общая а́лгебра, вы́сшая а́лгебра
群论 qún lùn Gruppentheorie [f] group theory théorie [f] des groupes [m pl] 群論 ぐ↓んろん тео́рия групп
环论 huán lùn Ringtheorie [f] ring theory théorie [f] des anneaux [m pl] 環論 か↑んろん тео́рия коле́ц
范畴论 fànchóu lùn Kategorientheorie [f] category theory théorie [f] des catégories [f pl] 圏論 け↑んろん тео́рия катего́рий
交换代数 jiāohuàn dàishù kommutative Algebra commutative algebra algèbre [f] commutative 可換環論 か↑かんか↓んろん коммутати́вная а́лгебра
线性代数 xiànxìng dàishù lineare Algebra, Vektoralgebra [f] linear algebra algèbre [f] linéaire 線型代数 せ↑んけいだいす↓うがく лине́йная а́лгебра
多重线性代数 duōchóng xiànxìng dàishù multilineare Algebra multilinear algebra algèbre [f] multilinéaire 多重線型代数 た↑じゅうせんけいだいす↓う полилине́йная а́лгебра
泛代数 fàn dàishù universelle Algebra, allgemeine Algebra universal algebra, common algebra algèbre [f] universelle 普遍代数学，一般代数学 ふ↑へんだいすう↓がく，い↑っぱんだいすう↓がく универса́льная а́лгебра
同调代数 tóngdiào dàishù homologische Algebra homological algebra algèbre [f] homologique ホモロジー代数学 ホ↑モロジ↓ーだいす↑うがく гомологи́ческая а́лгебра
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
代数方程 dàishù fāngchéng algebraische Gleichung algebraic equation coefficient équation polynomiale, équation [f] algébrique 代数方程式 だ↑いす↓うほ↑うて↓いしき алгебраи́ческое уравне́ние
代数式 dàishù shì algebraischer Ausdruck algebraic expression expression <mathematical logic>; integer; constant; variable; algebraic operation expression [f] algébrique 代数式 だ↑いす↓うしき алгебраи́ческим выраже́нием
代数分式 dàishù fēnshì algebraic fraction fraction; algebraic expression
algebraic operation operation <mathematical logic>
最大值自变量点集 zuìdàzhí zìbiànliàng diǎn jí Argument [n] des Maximums [n] argument of the maximum domain <mathematical logic>; maximum <mathematical analysis> argument [m] du maximum [m] 最大点作用素集合 さ↑いだいてんさ↓ようそしゅうごう аргуме́нт максимиза́ции
最小值自变量点集 zuìxiǎozhí zìbiànliàng diǎn jí Argument [n] des Minimums [n] argument of the minimum domain <mathematical logic>; minimum <mathematical analysis> argument [m] du minimum [m] 最小点作用素集合 さ↑いしょうてんさ↓ようそしゅうごう аргуме́нт минимиза́ции
二项式 èrxiàng shì Binom [n] binomial binôme [m] 二項式 に↑こうしき бино́м, двучле́н
系数 xì shù Koeffizient [n], Beizahl [f], Vorzahl [f] coefficient multiplication <number theory>; expression <mathematical logic> coefficient [f] 係数 け↑いす↓う коэффицие́нт
常数函数 chángshù hánshù konstante Funktion constant function constant <number theory>; function fonction constante 定数関数 て↑いすうか↓んすう конста́нтная фу́нкция, постоя́нная фу́нкция
constant term term <logic>; algebraic expression; constant
因变量 yīn biànliàng abhängige Variable dependent variable fraction; operand <mathematical logic> variable dépendante 従属変数 じ↑ゅうぞくへ↓んすう зави́симая переме́нная
等式，方程 děng shì, fāngchéng Gleichung [f] equation equality <mathematical logic>; expression <mathematical logic> équation [f]
偶函数 ǒu hánshù gerade Funktion even function function <mathematical logic>; line symmetry <geometry> fonction paire 偶関数 ぐ↑うかんす↓う чётная фу́нкция
identity equality <mathematical logic>
单位元，中立元 dānwèi yuán, zhōnglì yuán neutrales Element identity element, neutral element set <mathematical logic>; binary operation <mathematical logic> élément [m] neutre, élément [m] identité 単位元，中立元 た↑んいげん，ちゅ↑うりつげん нейтра́льный элеме́нт
自变量 zì biànliàng unabhängige Variable independent variable function <mathematical logic> variable indépendante 独立変数 ど↑くりつへ↓んすう незави́симая переме́нная
未定元 wèidìng yuán Unbestimmte [f] indeterminate variable indéterminée [f] 不定元 ふ↑ていげん неопределённый
不等式 bùděng shì Ungleichung [f] inequation inequality <mathematical logic> inéquation [f] 不等式 ふ↑と↓うしき неуравне́ние
代数分式 dàishù fēnshì irrational fraction algebraic fraction; polynomial; exponent
不可约多项式 bùkěyuē duōxiàngshì irreduzibles Polynom irreducible polynomial polynomial; factorization polynôme [m] irréductible 既約多項式 き↑やくたこ↓うしき неприводимый многочле́н
一次方程 yīcì fāngchéng lineare Gleichung linear equation equation; coefficient équation linéaire 一次方程式 い↑ち↓じほ↑うて↓いしき лине́йное уравне́ние
left identity identity element <mathematical logic>
monomial variable; natural number
奇函数 jī hánshù ungerade Funktion odd function function <mathematical logic>; point symmetry <geometry> fonction impaire 奇関数 き↑か↓んすう нечётная фу́нкция
parameter
partial fraction decomposition, partial fraction expansion algebraic fraction; polynomial
polynomial expression <mathematical logic>; coefficient; indeterminate
polynomial function polynomial; function <mathematical logic>
quadratic equation equation; coefficient
rational function algebraic fraction; polynomial
可约多项式 kěyuē duōxiàngshì reduzibles Polynom reducible polynomial polynomial; factorization polynôme [m] réductible 可約多項式 か↑やくたこ↓うしき приводимый многочле́н
right identity identity element <mathematical logic>
solution equation
square exponentiation <number theory>
system of equations, simultaneous equations finite set <mathematical logic>; equation
unknown variable
variable mathematical object <mathematical logic>
zero; root domain; solution

Abstract Algebra[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
algebraic structure underlying set; arity; identity
arity argument <mathematical logic>; operand <mathematical logic>
Boolean domain set; tautology <logic>; falsity <logic>
direct product Cartesian product <mathematical logic>
field set <mathematical logic>; basic operations <number theory>; rational number <number theory>
inverse element set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory>
underlying set, carrier set empty set <mathematical logic>

Group Theory[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
Cayley table finite group
group set <mathematical logic>
finite group underlying set; finite set <mathematical logic>
normal subgroup, invariant subgroup subgroup; conjugation
open interval interval
semigroup algebraic structure; associative property
subgroup group; binary operation <mathematical logic>

Ring Theory[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
ring

Commutative Algebra[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Linear Algebra[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
basis linear combination
characteristic equation characteristic polynomial
characteristic polynomial square matrix; eigenvalue; matrix similarity; zero
conjugate matrix, Hermitian matrix conjugate transpose
conjugate transpose, Hermitian transpose complex conjugate <mathematical logic>; transpose
diagonal matrix matrix; main diagonal
identity matrix square matrix; main diagonal
invertible matrix, nonsingular matrix identity matrix
linear combination expression <mathematical logic>; coefficient; vector space
linear dependence linear combination
linear independence linear combination
linear mapping vector addition; scalar multiplication
linear transformation linear mapping
binary matrix, logical matrix, relation matrix, Boolean matrix matrix; Boolean domain
like terms term <mathematical logic>
lower triangular matrix triangular matrix
main diagonal matrix; diagonal <geometry>
matrix rectangle <geometry>; expression <mathematical logic>
matrix addition matrix; addition <number theory>
matrix of ones matrix
matrix multiplication matrix; multiplication <number theory>; addition <number theory>
matrix similarity invertible matrix
proportional function proportionality <number theory>; function <mathematical logic>
rotation matrix linear transformation; rotation <geometry>
skew-Hermitian matrix, anti-Hermitian matrix Hermitian matrix
square matrix matrix; square <geometry>
system of linear equations; linear system linear equation
transformation matrix linear transformation; matrix
translation matrix translation <geometry>; matrix
transpose reflection <geometry>; main diagonal
triangular matrix square matrix; triangle <geometry>
upper triangular matrix triangular matrix
theorem in linear algebra
cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка
theorem in linear algebra
Cayley–Hamilton theorem characteristic polynomial; identity matrix; determinant; scalar; ring

Multilinear Algebra[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Universal Algebra[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

Homological Algebra[edit | edit source]

cmn-Hans-CN: 概念 cmn-Hans-CN: 前提 cmn-Latn.Pinyin-CN: gàiniàn cmn-Latn.Pinyin-CN: qiántí deu-Latn-DE: Begriff [m] deu-Latn-DE: Voraussetzung [f] eng-Latn-US: concept eng-Latn-US: prerequisite fra-Latn-FR: concept [m] fra-Latn-FR: préalable [m] jpn-Jpan-JP: 概念 jpn-Jpan-JP: 前提 jpn-Hrkt-JP: が↓いねん jpn-Hrkt-JP: ぜ↑んてい rus-Cyrl-RU: конце́пция rus-Cyrl-RU: предпосы́лка

480px-Quadratic_function_graph_key_values.svg.png

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Other Lessons[edit | edit source]

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