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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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13 Spazi euclidei
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Analisi e geometria 2By topic
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LEZIONE13-29:3.2023 To r n i a m oalleapplicazioniLineari. V,4spaziretoriali:V-> Wappl.lineare BbaseperV Clim(V)=m(xB:V- (RN) 2baseperdim() = m(Ay:N- 1Rm) V-Ne③ 29 I n ?���� ��m ����������������vistochetutteLeL:IR-SHMconodeltipo ·Com'èfattelematriceA?-A. pereesseretaleche(A(Xxx(ri)= x2K(v)FVEN Def.DateL:V- W B= {r;..., }- baseperVe2= für!,-.-,- mibasepar,chiamiamoMA TRICERAPPRESENT A TIVAdiL ME(2)= [(x7g).....)[CrTGM(m,n)I 2IElRm GIRM rispettoallebasiae2. TEOREMADIRAPPRESENT AZIONE- Sin L:V->W,Bbased'V,'basediN abra F= =Veika [(t)2= Mek)[r]B IR*.=M.(m,m)CIR2 TEOREMA(Nullte+rangogenerale)Ve HoIWSpazivettorialirispettivamentedi dimensionimedm. L:V-> W The[albradim(V)= dim(ker())+di(Im(L))Dim.OsbaseperVe &baseperW,M8(L)= A X(Ker())- Ker(A)= >din(er())=dim(er(A)) Xy(Im())= col(A)=>chim(ImKI)=din(col(Al) Quindidim(ker()+dim(Im())=dim(Ker(A))+dim(co(A))= =(n- r)+ r =n =din(V) Spiegazionedelteoreme - L:V - N X ~ ↓ -IxeIRm-> Im LA verv=Si(i= 0n)Xalün)=eiin : Xx(kerA)= {ntRYAi===(m)- def.diKer(A) 1) L:IP2-> IP ((p())= pi(n) &-42,a,x2)2:(2,x):matriceMe(i)? 1- [2]= (6)(x) = 0 [0]= 201 x- [x],= (2)((a)= 2 [17e:[8] a- (xY s[8]((x)=2x [2a],[2] m= Mex= 18.21.Quindipresop()= a +bx+ca +-c [pas]=1= [-(c)]MIasI= ==2][57-[quindi(((())=b.1+ 2cx = b+ 2cx che eeffetivamente= p'(x).
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