Video: GL n r yog dab tsi?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Hauv kev ua lej, cov pab pawg dav dav ntawm degree n yog cov txheej txheem ntawm n × n invertible matrices, ua ke nrog kev ua haujlwm ntawm cov lej matrix sib npaug. Pab pawg GL (n, F) thiab nws pawg sub feem ntau hu ua linear pawg lossis matrix pawg (cov pab pawg paub daws teeb GL (V) yog ib pawg kab tab sis tsis yog pawg matrix).
Ntawm no, GL 2 R txhais li cas?
(Nco qab tias GL ( 2 , R ) yog pab pawg ntawm invertible 2 × 2 matrices nrog cov khoom tiag tiag nyob rau hauv matrix multiplication thiab R * yog cov pab pawg ntawm cov tsis yog xoom tus lej tiag nyob rau hauv kev sib npaug.) (b) Ua pov thawj tias SL( 2 , R ) yog ib txwm pab pawg ntawm GL ( 2 , R ), qhov twg SL( 2 , R ) yog pawg sub GL ( 2 , R ) suav nrog cov 2x2 matrices determinant 1.
Tsis tas li ntawd, koj yuav ua li cas paub yog tias lub matrix yog invertible? 1) Ua Gaussian tshem tawm. Ces yog koj tseem tshuav a matrix nrog txhua tus lej hauv kab, koj matrix tsis yog invertible . 2) xam qhov txiav txim ntawm koj matrix thiab siv qhov tseeb tias a matrix yog invertible Yog hais tias nws determinant yog nonzero. Koj tuaj yeem pom qhov kev txiav txim los ntawm "cofactor expansion": pib nrog lub sij hawm a11.
Ib sab saum toj, yog GL 2 R cyclic?
Nws ua raws li S thiab T tsis commute; li no, GL ( 2 , R ) tsis yog abelian. Theorem 4.7 nyob rau hauv daim ntawv contrapositive tam sim no implies hais tias GL ( 2 , R ) tsis yog cyclic.
Tus nqi ntawm tus kheej Matrix yog dab tsi?
Tus kheej Matrix kuj hu ua Unit Matrix los yog Elementary Matrix . Tus Kheej Matrix yog denoted nrog tsab ntawv I × ”, qhov twg n×n sawv cev rau qhov kev txiav txim ntawm tus matrix . Ib qho ntawm cov khoom tseem ceeb ntawm tus kheej matrix yog: A×I × = A, qhov twg A yog square matrix xaj n×n.
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