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- Politecnico di Milano
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- Management Engineering
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- Analisi Matematica 2
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- Exercises · By topic
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02 Autovalori
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Analisi Matematica 2By topic
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29/05/2023Sia2:R3x R3elapplicazioneunari la 125/1/2018)calmatricerappresentativaaspettoallebon comonicaè A= j0]-conse a)DeterminariivalorediDucuiAèdragonalizzabilia)Stabilire,alvararediLER,sensteunderbasediR respectsallequaleoaltricerappresentatee dieèdragonali.a)P(x)=1- xI 3=D- II I (a- x)[(1- x)(0- x)- 3 1A-XII02xO (X-1)(X- 9)3 29- X (- x)(x2- 10x)= 0 X(x- x)(x- 10)=0 11=0 da=G Xz=10 Se2F0,10abbiamotreautovaloriemplicisonoregolari => seguechelamaturièdiagonalizzabile·e1= 10 x=0iregdarepeschesemplice(ma(0)=1),ment trix=edèdoppioprechiMalld=2.lex=0 ,x= 10èregdareperchesemplice(ma(10)=1)2 mentrex= 0 èdoppioprochema(0)= 2 Siad = x= 10 Xs=0 Xn=X2= i 58re10 -N87Tue - 9103 diV(0)=1-911= - 313M1= 1343 I08IMy=0 4Mg=00 Inquestocasola V)=2([])8= (53]}matureAnone dim(V(101)=1=ma(10)=2 diagonalizzabile siaA = x2=0MalO)=2 X3=10ma(1)=1 (A- 01)= Ru(A) 103A= To eI*= Trot088 ⊥M1=- 33 dei(0)=2 RuAo= 2(- 3],[-]) Fit]= Foje+5JmBamios= ([3],[5]} deiV(0)=ma(0)=>lamatureAè dragonationabilib)SeSFIDesisteuna basetalecheAsiadiagonale.x=101x= 0,53758773 1517) Baus=((5)"))BA-not)=((3)3HotrovatotheautorettoridellatrasformazioneLche,seso R3.obnarmenteapendentediteageneraronodetermmari unabasederAsiadiagonalecon2F10 IA-GIT- 1- 22 3 -Est29.2)1- 623 I0 6- g-glteeg0 0 0 · - 2)0 2F0CF-2=>diV()= 1 Pa=po2 Pa= P3 (1(1- 2)=- 2(18)- 33111-2)= psCp(1-2)= f3)- 6= p= Aes2+2 p= 0eP1= P5176)[B]:[emBanson= (5]:T8]:(il
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