Dab tsi yog pawg hauv algebra?
Dab tsi yog pawg hauv algebra?

Video: Dab tsi yog pawg hauv algebra?

Video: Dab tsi yog pawg hauv algebra?
Video: Lesson 6-English -Algebra-Volume IV 2024, Kaum ib hlis
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Hauv lej, a pab pawg yog ib lub teeb nruab nrog kev ua haujlwm binary uas sib txuas ob lub ntsiab lus los tsim ib qho thib peb hauv txoj hauv kev uas plaub yam hu ua pab pawg axioms txaus siab, uas yog kaw, associativity, tus kheej thiab invertibility. Pawg sib koom ib qho kev sib raug zoo nrog kev xav ntawm symmetry.

Hais txog qhov no, dab tsi yog pab pawg thiab nws cov khoom?

A pab pawg yog ib qho finite los yog infinite teeb ntawm cov ntsiab lus ua ke nrog kev ua haujlwm binary (hu ua pab pawg kev ua haujlwm) uas ua ke ua tiav plaub lub hauv paus khoom ntawm kaw, associativity, tus kheej vaj tse , thiab inverse vaj tse.

Qhov thib ob, dab tsi yog pawg hauv abstract algebra? Txhais. A pab pawg (G, ·) yog ib qho tsis muaj teeb tsa G ua ke nrog kev ua haujlwm binary · ntawm G xws li cov xwm txheej hauv qab no tuav: (i) Kaw: Rau tag nrho a, b G lub caij a· b yog lub ntsiab lus tshwj xeeb ntawm G. (ii) Associativity: Rau tag nrho a, b, c G, peb muaj. a· (b· c) = (a· b) · c.

Kuj paub, dab tsi yog pab pawg hauv linear algebra?

Hauv lej, a linear algebraic pawg yog ib pab pawg ntawm cov pab pawg ntawm invertible n × n matrices (hauv qab matrix multiplication) uas yog txhais los ntawm kev sib npaug ntawm polynomial. Ntau tus dag pab pawg tuaj yeem saib raws li linear algebraic pawg dhau ntawm daim teb ntawm cov lej tiag lossis cov lej.

Dab tsi ua rau ib pab pawg?

A pab pawg yog ib phau ntawm cov tib neeg uas muaj kev sib raug zoo rau ib leeg uas ua rau lawv interdependent rau qee qhov tseem ceeb. Raws li tau hais tseg, lub sij hawm pab pawg yog hais txog ib chav kawm ntawm cov koom haum sib raug zoo uas muaj cov cuab yeej sib koom ua ke ntawm lawv cov tswv cuab.

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