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- Politecnico di Milano
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- Energy Engineering
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- Analisi e geometria 2
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10 Teorema di rappresentazione
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LEZIONE10 22.3.23 Esempab:8) L:R-italeche Lx=A con A= Lost-sind Isinch cosdI*èunarotazioneinsensoantiorariodi Infattiserappresentiansit in ordinate polari,conaf27:Ts e âIallora I Altrocorocainaesit OSS- V,wspaziveteriali. B= {i,. . . .,tnybaseperV: e S:Sir;...,myCN qualsiasiI!L: V-> I applicazionelineare t.c.((vi)=wi fi=1,---;m InfattipreseIEVabbiamo. definiamo inci.ix:w e A COROLLARIU1-DativeWspazivettoriali ApI didimm Th.[albrarVeW now ISOMORFI(ILISOMORFISMO) Din.Br= {r'....,whye BN=für;..., }L:V--A-c. ((t)=w:fi=1,...,n INETTIVIT ALioeL(Ow):Orseguede indipendenzalinearediBr SURIETTIVITELie((V)= Vsagnedalfattochei generaW. VeWsono ISOMORFIEdim(V)=cim(A) ↑ COORDINA TE COROLARIO2- SeUhachmensionein e HbIB= {r?...,}iuna base, Th.[Alloraasstabilisceun isomorfismotraVel =V im x[]s*R~coordinatediv nellabaseB - sefficientidellacamb.DicherappresentiinB f.L'isomerfioronelcorollarioe dett MAPPAdelleCOORDINA TEe haindichiamo con XB,C X:V-> 1* xz(v)= [v]B- Esempio:R2&{,3 abbiamovistocheanche - &- E2-j I 3ebase2 Ine S met-I --2W wi Seprendeades. itretorei= 3i + 45 2 [3=[][d(verifare!)infarti- i(2=- j)+ (i+ j)= 3i + 45= i in= - 1Forti PROPOSIZIONE:Heremad'rappresent.perL:R*- x)Tu t t ele applicazionilineari1: R"-> IRM sono deltipoLA,con ACM(m,n)
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