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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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09 Nucleo e immagine
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LEZIONE9 - 20:3.23 APPLICAZIONICOTRASFORMAZIONILINEARI Comenon fattele funzionitra spazivettorialiche conservanoleoperationdicommae prodottoperscolare? #.DativeWSpazivettoriali una APPLICAZIONETO TRASFORMAZIONE)LINEAREeuna funzione(:V-> o taleche (n + i)= 2() tE,Vin+V FizV,1Gk-e 2(2w)= 12(i)·inV -· imW CNSperlinearità: :V-> Wélineare,(((Ai+ur)= 1((n)+ Mh(r) fi,rEV, 1,ERsiverificafacilmente- VeDOMINIO We'CODOMINIO; Esempi:Stabilirequalisonolineari 1)2:R2-> 12,L(r)=35 ⑮2)C:1R2- 2IR" I~Im [8]Lu2 es -([2]+ [E))= ([T= füri]= []T+ Analogamente(xn)= (((i))= (E)= = (ri)- as 3)L:- IPL(p())= p'(x)⑰L(b(x)+ n.q(a))= (xp(x)+ mq(n))= => Xp(x+ masa)=x((p(x)+ u((q(x)) 1)C:M-> RPLenon Ti] I↑ ( + y)= (in)= (wee 2 - xy)= []+ 737(w]II E5)2:12- 12 (127- In -kTT)- (D)- TET)- E 6)L:R2-RYLamAa ⑪A A AcM(m,n) ((x+ j)= A(n+ z)=Ax + Ay= (x+ 21y ((x)= A(x) =1 An= 1 Li 7)(:m(n)- m(n): AmAB- BA doveB=M(m)fissata- ⑮(1+ AY)=(A+ 14B- B(1+ 72)= = =(+ ((xA)= (A)B- B(xA)= x[AB- B)= x((A) PROPRIET A- a)L(8)=Wne b)((- r)= - ((ü) c)((i- F)= (() - ((t) d)((iii)= (v)DIM.a)((0)= ((n- i)= ([r)- ((n)= ow b)((- r)=((fe)) = - 1((r)= - ((r) etc. SeVEkENDOMORFISMO:V-> Vlineareèdetto DEF_i)IMMAGINEdiéIm(L)= {L(r)(veV]cW i)NUCLEOdiéker(L)=1- (0) SHerderivadaltermineinglesekernelper nucleo,ancheNCL)0 Null())
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