6.3(3,12,14,22) - HWIZ 1 Mafia [/3/ ASS/gnmenf /Z...

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Unformatted text preview: HWIZ 1 Mafia [/3/ ASS/gnmenf /Z 50/uh‘0n3 fiecfi'on 6.3 70:" vibe h/lowmj Inner larva/ud- space 1/ and hear aperm‘pr Tan V, emit/mica 7“ ar #29 Jaye/q vamp m l/: 1/: CE" , 7(ZUEZ) : (22. + £2). , (M) a.) x= C3—i,1+2;) 2. Le+/8 be #m Shana/arc! ordered éan': fir a: : . = L . .735 [T],3 I) and T [1.3/3 n .3 sasummhzfi] ~3s+iz :‘alfi-wag: y5¥€ «a, , @Le+ Vine an inner lowdud' Space, , and iei— T be. a finear o/per‘afi’r‘ mfiuf W 7%ng b) o \l :k ,\ k v u I ‘ ...N 01'.” w M + m N! w) u an V. @913;ng BCT*)J‘=N<T) 13;: 8(T*)i§-N(T)i xe RCT“)"‘ ===> mega—’0 ,(X,y>=0 as) Vvev I <29 Tm»: 0 =9 VveV) (70¢), v>=o = <0, v7 :7 T(x)=O by 773?” 6.19, =-> xe NCT)“ N7"? 2 NCT): ace MT) ==> T<x>=0 3”“? Vve 1/, <TCx3, v7 = 0 ==> We V) < x, TYVJ \/ = 0 —..=> xe R(T*)J’, Rn?“ = NCT). w Hle 2 @Q W I; V is fim'+e«olim€n;ional, fiaen HCTfl-‘NUUJ' ff 55”“? V "5 Fm?!" dime/mom}, 4M» .40 Is he AubJflQCQ 8C7”). Ken 80‘”) = (8 C7”“)*)l £3 Exercise [3(a) of Sedwn 6.2 ’ NCT) J" by pat/{- @ . 27 @id Vbe an innerprOdl/ld space, and let 5’ as V. flepne ‘7“: V-2V by 721): 0992 743/014“ xe V. Prove 71.5 linear ) Ta? eXI-Sfii and find an ear/UM: expnawl‘orz for it. ff. 18+ xi,X}_ 6V and c be asW. 772m 'TCCX,+ xz)= <cx,+xgly>z :(<C"uy> + <Xz,y>)2 b5 Pro/Der? ofi’medLoot ‘ C 09,502 +<xz,37z = a TCx.) + T09.) , T)? mats 9, 75m 6.? and we. know We V and WM: 1/, <T0<Lv> =<x,T*?»3; 50 <70L),V7= <<ij7zfll7 == <X,3><%;V7 = (Z)v><x/57 = <X,<2,v>y7 by 72,146.11: “’"<?<, <V,273> r <79 T*<v>7. =7 T*(v)= «02):; 7"f (70: (992)) Vxe V. a @(Q 4ind +929. minimal Aouction: x+g~z :O Le+ A= 3 ' ‘\ and. b= 0 2705 +E:3 2 -i i 3 I “I i 2 xwy +§=Z HWIZ. 3 3 o —e o g—R, l 0 "‘3 s O o 6 '4 o 3 > 0 6 H 3 q H 3 2. —2 v: 3 i 9— 8'4‘53 j ‘ __‘ -.— o > O a O i O 5 I o 6 H 3 0 a ‘3” :5: A 8 0 H 3 2 0 Li "3“ ‘7‘ "L‘Rz‘f'a‘fi’ [ G "-33— 0 o o l 2. J. @ u= .1. :‘S a AO’WLW’L‘ “3" a 2- O O o o 0 . . . \ - - A* - I 2. i Q “ ‘ H Whom Aolwfma is 3- LL - 1 ~ i W , ‘5 —: ‘2': ‘ '3; -3 1 l of; .1. 2. Semen 6.“ @(B W 053) T<a,b,c)= C‘a+bJ55»‘M*Zb+5C> Lé‘f'fl: 2(110/0)1C02]10))(O’0"I)} TC/,0,0): ('ixoaq) 7(0150): (1,552.) 710,011): (010,5) 5:; [TD/3: —0I 5100 . 53 7Zm6.iG,CT*]/3=ET]’$*= *I 0 ‘4 ‘1 —2 S l 3 -z o o 5 Since. [71,3 7” [71]};F , %&n TfiT” ~40 7'19: n07“ afie/f-acf/oiflf'. HWi2 if 50 mp m; at U ,3" [73,3 ::> TT" 31$ ‘7’"T 4:7 Ti: 110+ no/mal. oFV 83 77,7"; 6.16, 6.1;) ,3 an Or-fhonormal Aasi; (of agent/95%,;- 0/2 7-. @@ V‘W’fi) ; TC9):¥' , (9,3): I: R5560 0H: 83 Exercise. 2c Sec-iron 5.2, M tar-{fionormal Jar/‘5 755/ 1/ 1:: /3= 2', 25mg), 4f? (find-la} (5+ar+ (of-1‘41 #72 mande Aw“: Emmy-j anal manna/(«‘32. , affilymj #11. Gram~5chmfalé men/14005). M,A/mj/ar vb [pa/1‘ C69, Due/we #:aé- TCI):O T(2J'3‘(x~§-_—)) : 24? = J72 7( 6E Cx"—zc+-é—)) = [if-‘3: K ~ 6E =' [25 (X ~39) = $66 (mom—2:3) O : 0 $2: 0 “(1 ’¥ : O 0 O 3 EH” 0 0 523 a DUI? :2. 0 O o o o 0 JR? 0 :9 T7“??? 7"“7’ :3» 7’ is hof' normal. ’- 59 75mg 5.5é, 6J9“, ,3 M orflanO/MM AMI} for V of Elth‘fhd 0’07, [11/1/12 5 Le+ T62 51 normal operava on a flm‘k'oamwianwl wMLex [er [mow/d Aface 1/) mo! Left/V At: a AW’PIZCQ 0/ V« CM IfW is F/‘nvarian'l’, #78!) W [5.41/50 7‘”~,’nvarz'an+. ff Since. Ti; 61 normal operm‘or an a fi'nh‘f‘c/imcnjfofla/ comp/6X inner pmolud space V, by 75m 6J6 3 an owl'honorma/ Aasrs 7%,— l/ unfit-Hag of eigenvecv‘vrs of T =9 T is diagonalgab/e (by firm 5/) 75m 53 Exercise 2a of Sec. 5.4 , 72/ i3 axajonugaaxe \‘ a. 1 . n §.. 7 - ‘- a HW i2. 6 fiech‘on 6.5 @ 70/“ #26 mafn‘x 24, find an odhojo/m/ 0r unfi‘mgf mamk P 41:61 a ct/ajonal matan D 5.1L Fae/H): D. 0 2. l =A. @ 2.0 2. Z 2. O 048+ (A‘fI;)= A“ f“: 24:12 : ~t oie+ (-1: 9-) -2 de+(2 2>+zde+(z 4? - 2_ K2. 2 -t f 2 “‘3 2‘2 .-. —t{¢‘“-14) -2 (-15—q)+2—(‘I+2_£—) ‘ "6(t+2)(£—2)+H (n23 M (5+ 2) = 0H2.) [~e2-+2.e+3] = (1944-3 C~f+lfl (H2) 3 ~ (15+sz (154!) Engean are A,=~2. (mac/(hpb‘u‘tg 2.) 2b,: ‘4 Qmwbh‘puu‘ég :1.) NOW WE finch/he, bWeofor: EA, N(A+z:)= ~(iz 2.) = (4)5 + 911% : 3,19 e/R 5w fir E)“: = {WM 0 “’8 We W Grimm—SM)“; in {flat cm ormm 5mm; ‘1 “tw‘: (ti—LO) V2: Wz,‘ <W2., Vz> V; 3 (9,0)”) '~ <(iJ 0J”‘>z(!f"2 03> (35-910) mm (5)2 :— !o- - ’ ~ “ ” C’I‘O TC“ I10) —— i3é‘)~¥g)~— 45(1));“ZJ HW 12.? L: —L-(3)~3JO) WV,“ 5 nun 3 2. (A 2’3 FTC H 3 An odhonormml baAI'sfor ENQEFKJLZ— (5—), 0) , 3%.0, L43} : - = N ~ _ ; 53% ~04 qr) 233-1: __ § (5)16 tefi} Z 2. 44 3 '. fin orvrhonormwt basis £2er: fgz: {a )50} 7716 an Orv‘honorm 4L écw/‘s fir V con/112%? cf enuecfvrs of T ,3 z _._. h J”. _ *L‘ ‘- 4‘. fl fiIU/gl ‘ E 'J 0)) ’J )5“ C’J} MP=357 P HIM/2 8 M A be an mm Goal Sdbmmefivb 0r (om/Mex mar/rial may-Mk. QM frUU: E§Ag and fr (A*A) -‘ “Z” [A41 2 where. %e /\;’s are. Me (007’ ham/radii gamma) 6/3va of/i, ff S/me A is f‘fa/Aymmev‘fl‘c or complex normal I 3 a (minty mafn‘x I9 aural a diagonal ma+rfx D A-f- x9: Pm F. 756 diagonal enfn‘u of D an: m ZIyLnVa/W A; of A. army‘s/v (Np?) =z‘r(fl*wm) :ér Hump“) = H (MN) “’3 23* Q?) = érnCD) as P i; may = A; .. WM): . Now, NA: (P*DP)* (VD?) = P*D*P P"‘DP z PAFDj‘D P M i’ f; uni-hug 50 tr(A*A)—‘ tr- (WNDP) = tr ((P*D*)CDP)) = tr (CDP}CP‘D*)) (4,5 2.5] @ again) = {rib/910*D") M P [5 un/‘i'arg " g /‘\:/\; (Sum of m Mayo”! em)“ 0% w") 3 E IN); 2—: A fr(A’¥/°*): 2M1”. -—» I'D ...
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This note was uploaded on 01/26/2012 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Spring '10 term at UCLA.

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6.3(3,12,14,22) - HWIZ 1 Mafia [/3/ ASS/gnmenf /Z...

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