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GILBERT STRANGMassachusetts Institute of Technology

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Hedl|}'lro Koirrc, T.O.1527, I 1 10. 7 Tt),. (081) 394235, 394236 Fax: (01) Ariva: M'ials5,10681. Tt),. (01)38183?2,Fd: 3301581 xa! e-m!il: Fk@iesl.fonh.8r pek@physics.uch.gr URL: hnp://www.pk.uch.gr.

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CilbnStrutr Lircd Algcbn andits lrd applications, cdition @/98a Harcoun Bracc Jovlnovich, PublhheB yt.Iill'.1 ny*i yL(rddar n^NEruriHMrAxEr EK^o:E|) KplrrHt @ 1993 nu.nq txdoot Orrd6prosl9e5 Zti$e4 tfioon Oxrd'6ercs1996 Teit,t t"6ottt: M&ercs 1999 Alt.;doott otu dJ,trt ti: n.ieE ndpq os Ka0rnfi riEMdonf arLr.on Tprl.L fla!/Iio! KeirlN Telr"i Enryllut $tuqeaor(r ArlFirensKoeoy!awd,{$,NixoE TlavdartTOY METAOPA>TH

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IIAPAAEITMA 1

2 i1 1 l 12 3l f l -r o l =l+7 x ool ol 0 l ls L4y',v6pevo fla roQd6c!"/po, olorleio 1? eivor (2)(1) + (3X5), 6t1".to rorrlreqrx6 ro qs ne6rqE ]aapF{E p rlv nQ6q o4}un. To 8 etvar (4X2) + (0)( 1) ori6 1rl aernepq lpq4rri x 6).!s rLEZr).].s C, nsarnr6osrs, a.2a EEt}.'im yrdri t 1 cni ,l oetiol'o(r vandemonde

"i'":, lil i; ;llll= - /)C EiloL 6uv(tov F6vov6tor D = 0.

ll 1, br ,r l1 . d dl' Ll " "r ,il* :.r.E.: E:!r@o'ldur or i7.o\r. iia(?( tr x n.

:ror pDno:Fo L rD^13Dlou (u ot 9!,.Dtr^31i9lDl3) rDx d :o3o?gDt3i srxD^l,l 5ol1orcF D o 'Z) oro (u rZrI) or r319oDt3ri (t "e lror:!g,,p$li !rxq{o1r H m^F boll " '(r - cxq - rXD - txq - x)(o - )')(E- q)='A ^tr.l tr |?urqxodll '0I Z t Lrol.o.ov gultrso oor Er ol?dDrdno^ot 5Dt q)]orodoL'dx, = r nx q = r'o = t n o t$?wl lr^F odn goyo], 01grnD FD 'mx r sodr tu onn^qnlor,91 gnti rr^F D^ r3r!?0,r|dit : HinH\ cNvlra vLI

169

lox 6) tlllJl.adlcft &t oL Lbtorqras C ,rqaiEt!o .Fqavilo\{oL d!{i le"Yrl awte'turv oqLoFdlv. = ^(Dr) 1) Ai&. cn !0siagotr av c' =.rr tor c(Dr) 5.6.7 Oroeim onotov6rtror,4 xot Flc l1rluio ninFbl oraoq'i' [I:

fn 6 .l A=l,t P Jl, Ls n i.l

rr=l

fcos/, sin0 0l np L 0

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A|CIa!ff rn I.)vic 0. ror dJott !a Fl6viofts rc otorxio ot'l edol (l l) 'o! triv(x'r Aw6! o Fll6slrolos 6! owxi!Iar nzo).o. 6Lo1 or orqoq6s nou I4t.ioq |$v!zo crrl troEiow F$aa oq eaorl rou I zor tou i' 0o aqraoretwuv ro "o pio 6raY6aLd Bd'io dr6 'I! xiqLq xat !o o)'oBl'la6so1|pt npt,rern r.uia. o! pnoaonoap' n"r tbrorqtdr!pe 6nq{r0.r'xo tadrio Anqoa'flki iov rrcL,),yLoyo",p'ioow 1o!. 0d 6aioxol' q qils ro' ?r sdL !o 6onFiq L6LortpiE vtr 6LclovLo:ro(oorpe ro! rolurvttro! de(.4-)1) )Qlouoaodvra! (roxi.t.|mrxd t'roaYoalais oilr' aoo oei(orv ro cosr, x{i1| a6nvaro! = s.6.E no'os nivqras 'r/ crLLdltLfll 6dq vl = (1,1) v1 = (1'4) oril 6doll 11 (2,s)' rd vr r{n ri od!oNbuoolotl! = al.a)i Or onirrE rou rr naoxnnro .xqqdlot{(rs "r s.6.9 fro tK i6s 6.io'q,etqedoft to 6d{o8d (3.9) o(! g1lv6lcouocrri +'2v? rc069 erio xat ocv rlrr r + l:rr' Endtrl0s!@t oerOpryrtd6( o rrl o366tr 1o ' F to d: _'r:.u:' vr = 5.6.10 Efler6aruorf rlv lrlruro,( douryrl oi.lP6erxri E{iv vr = "'r" r = 1 1 2T O r ttsd o l o v l o F ( r 4 . nil./t r r,.)(r = lr x(r 4r7l'l i rt2i' .ril +.:la aut,ilfr +.11t2 rowilowoL Auro!.ivat o runog of_)'(fk 6dooE' s.6.ll Eiiv o petsorill1oflopo! ?- t!g| prd ovdxlcol oE ireos loeic llioEoE 45' iotr rua6o!,6a.iu loa riaoadr 10! oE neos t'l o!"vllq 6doi ul = (1'0), !2 = (0'1) zo(;E .ricnl! ad ox naq rd r1 = (1,l). vr = (1 1). a'iFs &! ot riv(reE auoi xtiee tLriwopc cor Eam6 1o!: ?r = r' 5,6.t2 O rtrtotx'. l.tuo1q4afu4uiq me)'veL Bqsir 10! otiGotxo nirdx(l,6ra' 'l re6q 6dol eivdLa = (1,2)' u = (3,4) ?d' 4 varo6l) = (1,0), u, = (0, l) (^v ivor o tanottxq beueon 6dq ri"at "'r 5.6.13 H traadfo'yogrotl a + br + cr2 tiaor t' + 2.r + 0r3. o) Karayadl'r roa 3 'It 3 ri\,ato D Yta to' onoio rox!t

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y) nots i1,ar rbrciqlls 1|arro ioLob|d\,roFaro or ro! ,i = = 5.6.14 AiErdtl o p.roorrtparror'6r v6 o l(t)dt 6sv 6xrr6'or4rds, "[0' .f/dr iXErxde oeropo sor r6rcrurt. Or orJvoarioEosoqorrlror 6rr oQi(ovra' tta "J(.) "/(r) s.6.15 :ror r6eo tuv rrvrix@r 2 ni 2. dot0)'.l o Fe1aoruaflofo< rou cvqoredqrxdo vdra. Beeire fls rbLo f6q ,{qr rorE 'lbLonila.,{rr" ro! r (tor! trivdiEs rox rxavo'oLonvA7 = -\A). s.6.16 d) Bairr 6!a! oa0oydrvto dloLdor Q rAQ =,^, do! Q

/=ll

ll

l 1lI I roL A=

Lr r ll

l0 0 0l l0 0 01.L0 0 3l

Ba.iir xot6Ew 6!a tljrEeolrlyos oeooxdvorla6v r6to6tawopri'rr,n r2 r1, qq'\-0 6) EnaLte].jor r dxqeoor P = 'rri +rri,j ilar n l6rd rat y'a r( 6no !nir. orr 5.6.17 ^.tft., o 6!0 6fipalt!. 6111tdg. oa1ory,rabtaioE nivardE ,4 eivqt 6royovLoroL'ioLFos: o) Edv oL t rcr Lr ivor oQeopolablaior, i6to rorit x lraaoaT =U tAI/. ro 6) E 09 dr(l) raryorrxos rcr iroL oAooFovd6raios ivar 6ro16vLos. 'Emrq " orr o rerlDvL'rG 7' rilar A 1t(lt 6rr rde oAoopovo6roio< rtvdx.ls {Fr 6iiqoemzdc i rI r6ronFi() iIrL ivq r},i$c orJvoi\ordto6rdwoFdrov: {.f r,lU =,^. O}\ls or r6'or+is Lxuvororouvqv l.\l = L s.6.1E aas|r. iva lcvovrxd Jtildxa rol, br! fi.!o! Eegrtralos. alatsEetLrLoaos, opeoFova. 6l(fos tt 6l.1y(;!ros.AriEt 6tL 6IoL ot nLa(aesrerq06oros ei!d! xclolrxoi. s.6.19 Eoro o1? si.varalas .i!o rary.)ltxdg nivaras 3 fli 3, p ororxEtcti'. t]Jytail.lte ro otorlei{r r!)v ??t xar rrlr ncL teiEre ou edv ivar ioa, i6rr o trA6ner.',a ri.',ar6lal(ix,rcq. " 5 . 6 . 2 0E a v o . \ ' s i ! d ' r o v o u " o < . b e r E f to l t N r l = | . r F r , . f l u xdo. i'rLdvuoFo r. :4d.Odvdr ofl rl, leorpi roll N axrx io i6ro frixoE pe 14! i orri),r. -t?t@ol: Ed! o N 0iraL eflio4E (dru) reryovLxoMATA

3,2n Ew KH = r (awFEafrrtavds), i6I' or r6,orrpls ivo, qowomrxts ,{ar ra rdro6raruoparaoaooydJvrd. d) I16s ,IvoaiErr&r o Il - I ilqr awtmqh!+ro!; 6) nd4 yvoeiEer(iT| r{ = LrAUs 1Laivcv osoopova6roto Jrildl{o y: 'r) l'lari o e^r eivor oq0otorobroioqi 6) l"rcti o eK' eivar op0oporo6rcriost 5.21 Ed!orrliroroiroy6uosrivorss!ooL1ciod,rr'?,/.noLoseiv{llo,l,/rArr/ xat roLts iraL o! r6rorqd6.610!

ti il5.22 Ed\ 42 = -/, ro|s eilor or l6Lo fi( rou ,4i A0iEre61t to n ne6rsr vs oivor detrc. dic! o A slvdr ftea.rpaI|xd'( ntlar(ls i Etrl n aor 66m noadbr,ylq. 5.21 Eda ,4x =.\rr rar ,4?v = ):y (6lc rpoyFc rd) 6eire6rr r"9 = 0. s.z Mc traeoD,oTrt to! rilqxo Fourier .iaar o rilo.ras olvttFrrouo!'

j

3r'l I sird sin20 sin

V2 L.in3, sir 6t $in 9rl

'in6rl Fr d=;

Enrd,rl0slorort Sr = S-r. (Or onlldg ivqr rd |6Lo6|anJolala ro! tAficlldvrc! nivaa( -1,2, -1.) o) Basirr trl p1l5vrx6 rivdxo N ps Nr = 0. 6) Edv Nf = ,\r, biltr 6rr ro .\ roaner ro ivdr Lq66!. 'y) Alli 6rr o N (ovopo(6pr!o< "lt)6.vo6wapoE 'rt!axas") 6s! proasi vu ivar

5.26 a) Bpeirr ror r{vora P = ra? /a'a nor npo6dner rdo 6L'iwopa orlv r!0iq 6tdro! o = (2,1,2). 6) noLa Erlar I Fordbrri u r$rvL"ri rbtonFri rou P xdr roro ro ovriororto

'y) Auote to r^.,r = PLr Erl.|r6vrus cr6 ro,0 = (9,9,0).

s.21 Yroeaor 6t. I rEi'qBqirerov /.

1aa|r|rti toD ,a !ivs! (?, 6) rar o! !6Lofllds ro! rivor i, -t.

5.2t

(l) rLd nor.6 r+rq iov c xor d, ixer o ,,1ned.yportu6s !6Loflt'ds ror oe0oy6!L{t D|o6ldvlofarci

11 2 0l A=12 d clL0 5 3l

6) rtd notd . aar d Fftoaoi$ aa 6eofu roia oqoozdrouri iva' (mduooloi iov oql6v (plv ro.rd!ftrl):

bl(rvtiol(lra ftou vd

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5.29 Ed! r( cviotrola ir rorodL(.!un01a turv

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ro! 5. noL.; iacL ot t6Lorttric l('

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