Linear Algebra with Applications PDF
Preview Linear Algebra with Applications
WorlHde adquarters Jone&s B artlLeetatr ning 5W alSlt reet BurlingMtAo 0n1,8 03 978-443-5000 [email protected] www .jblearning.com Jone&s B artlLeetatr nibnogo kasn dp roducatrasev ailtahbrloeu mgohs bto okstoarnedos n libnoeo kselTloec rosn.t aJcotn es & BartlLeetatr nidnigr e,cc tall8yl0 0-832-f0a09x37 48,- 443-o8r0v 0i0so,iu trw ebsiwwtwe,. jblearning.com. Substandtiisaclo uonntb su lqku antiotfJi oense& s B artlLeetatr npiunbgl icaatriaeov nasi ltaobc loer poratpiroonfse,s sional associatainodon tsh,eq ru alifioerdg anizaFtoirod nest.a ainldss pecidfiics couinntfo rmaticoonn,t atchtes pecisaall es departmaetJn otn e&s B artlLeetatr nviintagh aeb ovceo ntaicntfo rmatoiros ne nadn e mails pteoc [email protected]. Copyri©g 2h0t1b4y J one&s B artlLeetatr niLnLgC,a, n A scenLde arniCnogm pany Allr ighrtess erNvoep da.r otft hmea terpiraolt ecbtyte hdic so pyrimgahybt e r eproduocrue tdi liiznae ndyfo rm,e lectroorn ic mechaniicnacll,u dpihnogt ocopyreicnogr,d oirnb gya, n yi nformatsitoonr aagnedr etrievalw istyhsotwuertmi ,t tpeenr mis siofrno mt hceo pyriogwhnte r. LineAalrg ebwriatA hp plicatEiiognhEstd,hi tiiosan n,i n depenpduebnlti caatnidho ansn otb eeanu thoriszpeodn,s ororeo dt,h erwiaspep rovbeytd h eo wnerosft hter ademaorrsk esr vmiacrek rse fereinnct ehdip sr oduct. Somei mageisnt hibso ofeka turmeo delTsh.e smeo deldson otn ecessarilyr eepnrdeosroesrnpe ta,,r ticiipnta hteae c tivities represeinntt heeid m ages. ProductCiroend its ChieEfx ecutOiffivcee rT:yF ield PresidJeanmte:Hs o mer SVP,E ditor-inM-iCchhiaeJefol:h nson SVP,C hieMfa rketOiffincge rA:l isMo.nP endergast PublisChaetrh:l Seeetnh er SeniAocrq uisiEtdiiotnTosri :mt ohAyn derson ManagiEndgi tAomry:B loom DirecotfoP rr oductAimoynR :o se ProductAisosni stEainlteW:eo nr thley SeniMoarr ketMiannga geArn:d reDae Fronzo VP..,M anufacturainndIg n ventCoornyt rTohle:r eCsoen nell CompositNioornt:h east ComIpnocs.i tors, CoveDre sigMni:c haOe'lD onnell Righ&t Psh otRoe seaArscsho ciLaitaeBn:r uno Righ&t Psh otRoe search AsGsiinsLati acnatt:a CoveIrm ag©e :j ordachuet/tSehrStIoncck., PrintainndgB indiCnogu:r iCeorm panies CovePrr intiJnoghP:no wC ompany LibraorfyC ongreCsast aloging-in-PuDbaltiac ation WilliaGmasr,e t1h9,3 7- Lineaalrg ebwriata hp plicaItG iaornesWt ihl lia-m8st.he d. p.cm. ISBN9 78-1-4496-(7c9a5bs4oe-u 5n d-)I SBN1 -4496-79(c5 a4s-e4b ou1n.dA )l gebrLaisn,e ar-TextIbT.o iotksl.e . QA184..W2552 014b 512'.5-dc23 2012012118 6048 Printientd h Uen itSetda toefAs m erica 161 51 41 31 2 109 8 7 6 5 4 3 2 1 Id edicthaist beo okt oB riaann dF eyza vii Th it.esxti asn introd uctiont.o LineAalrg esbruai tfaorba cl oeu russeu aoflfleredy a t thes ophomore levTehle. .materlal imsa ngeidnthre e parts. Part 1 consoifws htast Ir egaasr bda smat.eriiacl -discussoifso ynsst oeflm isn eeqaura tivoeern.so,ir ns Rn( inclthuedco inncgepts ofl incombinateion,a r basainsdd,i mensimaotticesn,) ,linear transformationdeterminsants,, eigenvaalnuedesi ,g ensapsaw ceesla,lso ptioanpapll ica ti.ons. Part 2 builds onth imaterisa l t.o discguensesr al spacesv,ecto rs uch ass pacoefms ati i ces andfunction s. It inclutodpeiscsus c ahs1h erank/nul lity 1heorem. inner producatnsd, coordinate .representationsPart. 3c ompletes thcourse ew i1hs omoeft himportanet ideas anmethodsd inN umerical LineAalrg esburcaah si lconditiolnin- g,p ivoting, LUd ecom positioSni,n gaVunaldl aDecourme po sition. Thieditions continues thetraditio n ofe arleideri tbiyobe nisna gfl exibblleneod ft he ory, important numerical techniques, aninterestding applicTahtieob nooski. sar rang ed aroun2d9core sectionsThese . sectioinclnudes topitchsIa tthink are essent.oti aanli ntro ductory linaelagre coursbreaT. heirthense ample time fort hien structor to selfurtherec t topithatc sgi vet hcoeu rstheedesired flavor. Eighth EditionT hear rangemoefton pti icthsse s amaesi nth eS eveEditionn.th Thev ec t.ors pacRe" s,u bspbaasesce,s ,a nddi menares iionntrod ucede arl(yCh apte1r)an ,d are theuns eidna natural, graduwaya lto discsuuscconceptssh aslinear transformations inR" (Chapter2) ande igensp(aCliapterc es3 )l,e adtoi generaln g vecspacest or (Chap4te)'Ir.h e level ofabstract ion graduaincreasllye sa so npreo gressiensth ec ourse-an dt hbei jgum p thoaftent exisftorss tudienngts o ifromn gmaJrix algetob grean ervectora l spaciesnso longtehreT rhefirse. t threec hapgitervse t hfeo undaotif1ho evn ec tospra ce theyR 11r;e ally formafa ircolmyp leteelemen tary minicourse forth ev ector spaRcneT. h reste ofth ecourse builodnsth isso lfiodu ndation. Changes This editiisaor ne finemen to fth eS eveEditionn.th Certain sectiohnasv beee n rewriotherstte nad.ded, andnew exercises have been included. Thaime has been to improve thcel arifltoywa,,n sde lecotifmo anterial . Thed iscuosfprs oijoenc tiionnSs ecti on4 .fo6r, example, habesen rewriTttenh.pe r ooofft hGrame- Schmidt Orthogonali7.ation process is nowmore complete. A discuosfsorthogon ialo ncompleme nts inan ewS ection4 .n7o w leaidnstot hOret hogoDecomponsiatilo n Theorem. Thet echnoifQq Rufactoriz ea tion has nowbe enincluded andt himportanece ofth e method for computing egenvalueis isd iscusInse dr.e sponstoe numerous requests, I have nowincludedaninttcduction to Singular Value Decomposition, wi.1hadiscussioonfi tsi mpor tancefor computing ther anokfa matrix anda co nditinoumbern for a matrix. Thesingular valduies cualsssogeneralii zeso n thconcepte ofps eudoinverse introducedi nS ection 6.4, XVI Preface leaditnothg e b roader disocfluesasssiqtou na rseosl utoifao nny s ystoefml ineeaqru ations Sectio6n. o4n L easStq uareissa lsnoo wm orec omplete. Finalwleym ,e ntithoant s omen ewr eaalp plicahtaivobene se and deIdi .n cluadb ee au tiful disocfuL sessilMoianet ricfoerse ,x amplea,n di llusthroawtt hee smea tricesl eatdo long-tperrme dictoifbo inrsth asn d deaotfah nsi maBlirthss. ands urviovfap lo ssumasn d ofs heeipnN ewZ ealaanrdde i scusTsheedm .o deuls eesi genvaalnudee si genvectors. Alternate EighEthd itioThni si san upgradoefth eA lternatSee venEthd itiothna tn owi ncludes topics assQu Rc fahc torizatSiionng,u Vlalaure D ecomposiatnidofurt nh,e r intereasptipnlgi catioTnhses. o phomore-llienvealeargl e brcao urcsaen b et augihntm anyw ays-thoer der inw hictho piarces o fferecda nv aryT.h eraree merittso v ariouasp proacohfteesnd, e pend ingo nt hnee edosft hset udenThtissv. e rsiiosbn u iulpto nth es equenocfte o piocfts h peo p ulaFri ftEhd itiTohne.e arlier chaptseyrsst eocmfosl v ienree arq uatiomnast,r icaensd, determinants-mthoer ea bstramcatt ersitaartlsl atienrth i sv ersiTohne.v ector sRpnia sc e introducienCd h apt4e,rl eadidnigr ecitnltygo e neralv ectsopra caensd l inetraarn sforma tionsT.h ialst ernavteer siiosen s peciaaplplryo prifoarts et udewnhtos neteoud s el ineearq ua tionasn dm atriceisn th eiorw nfi elds. TheG oalosfT hiTse xt • Top roviads eo lfiod undatiinto hnme a thematoiflc isn eaalrg ebra. • Toi ntroduscoem eo ft hei mportnaunmte riacsaple cotfts h efi eld. • Tod iscuisnst ereasptipnlgi castoit ohnasstt udemnatysk noww hena ndh owt oa pply lineaalrg ebArpap.l icatarieot nask efrno ms ucahr eaassa rchaeolcoogdyi,tn gh eory, demograpgheyn,e tiacnsdr, e lativity. TheM athematiLcinse aarl gebirasa c entrsaulb jeicnut n dergradmuaatthee matMiacnsy. importtaonpti mcuss tb ei ncludientd h icso ursFeo.re xampllei,n edare pendenbcaes,i s, eigenvaalnudee isg envecatnodlr isn,e trara nsformatsihoonusbl edc overceadr efulNloyt. onlayr es uctho piicmsp ortiannl ti neaalrg ebtrhae,ary e usualal pyr erequfoirso itthee r coursseusc,ah s d ifferential eAq guraetdaietoa nolsfa . t tenthiaosbn e egni veinnt hibso ok top resenttihn"egs tandalridn"ea arl gebtroap ics. Thicso urisse ofttheens t udenfitr'scsto urisnea bstrmaactth ematTihcess t.u desnhto uld notbe overwhelwmiethdp roofbsu,ts hould nevebrett haeulgehhsotsw t op rovthee orems. Whenc onsideirnesdtru ctipvreo,o offst heorearmes p rovidoergd i veanse xerciOstheesr. prooaref sg iveinno utlifonrme, ands omeh avbee eonm ittSetdu.d esnhtosu bledi ntroduced carefultloty h arte ofd evelopainndwg ri tinpgr oofTsh.ii ssa tt hhee arto fm athematicThse. student sbhetraio nueldd t oth ink" mathematicFaolrel xya.m"p lthee,i deoaf " iafn do nly i"fi se xtremeilmyp ortianmn atth ematiItc arsi.s evse ry natiunral lilnyea arl gebra. Oner eastohna lti neaalrg ebirsaa n a pproprcioautreis new hictho i ntroduacbes tract mathematitchailn kiistn hga mtu cho ft hmea terihaalsg eometricianlt erpretaTthieso tnu. dencta nv isualriezseu lCtosn.v ersleilnye,aar l gebhreal pdse veltohpeg eometriicnalt u itioofnth es tudent. Geaonmdae ltrgye bgroah and-in-ihnat nhdic so ursTeh.ep roceosfs startwiintgkh n ownr esualntdsm ethodasn dg eneralialzsioarn igs ensa turaFlolrey x.a m 2 3 plet,h per operotfiv eesc toirnRs andR areex tendteod Rann,dth eng eneraltiozv eedc tosrp aceosf m atricaensd fu nctioTnhse.u seo ft hdeo ptr odutcodt e finteh fea milainarg les, 2 magnituadnesdd, i stanicnRe si se xtendteoRd n .In turn , thsea mei deaarse u sewdi tthh e inneprr odutcodt e finaen glemsa,g nitudaensdd, i stanicnge esn ervaelc tsopra ces. ComputatiAolnt houlgihn eaalrg ebhraasi tasb strsaicdtie t,a lshoa si tnsu merisciadle . Studensthso ufeledl c omfortwaibtltheh ete r"ma lgoribtyht mh"ee n do ft hceo ursTeh.e Preface XVII studepnatr ticiipnta htpeer so ceosfds e termineixnagc twlhye rcee rtaaligno ritahrmmeso re efficitehnaton t hers. Fort hosweh ow istho i ntegrtahtece o mputienrtt oh ec oursaeM ,A TLAB manuahla s beeinn cluidneA dp pendDi.xM ATLAB itsh meo st wiudseelsdyo ftwfoarrw eo rkiwnigt h matricesT.h e mancuoanls iosf2t 8ss ectitohnatsti i en ttoh ree gulcaoru rmsaet eriAa lb.r ief summaryo ft her elevmaantth ematiisgc isv eantt heb eginnoifne ga cshe ctiBouni.l t-in functioofMn AsT LAB-sucahs i nv(foAr)fi ndintgh ei nverosfae m atrixA -arei ntro duceadn,d p rograwmrsi ttientn h MeA TLABl anguaaglesa or aev ailaabnldce a nb e down loadefrdo m www.tsetson.edu/-gwilliamT/hmepfi rloegsr.ahimtnsmc .l undoeto nly computatipornoaglr asmusc ahs G auss-Joerldiamni nawtiithoa nna ll-sotpetpisob nu,at l so applicastuicoahns ds i grapMhasr,k ocvh ainasn,da s imulastpeadc e-timveo yagAel.t hough this maniuspa rle senitnte edr mosfM ATLAB,t hied eassh oubledo fg enerianlt erTehset . exercicsaenbs e i mplemenotneo dt hemra trailxg ebsroaf twapraec kages. A graphicnagl culaaltsocora nb eu seidn l ineaarl gebrCaa.lc ulaatroaerv sa ilafobrl e performmiantgr ciox mputatainodfon r computing ercehdeulcfooerndm sA. calculator manuafolr t hceo urhsaes b eeinn cludienAd p pendCi.x ApplicatLiionnesala gre briasa s ubjeofcgr te abtrea dth.I tssp ectrumr angfreosm th ea bstract througnhu merictaelc hniqtuoae psp licatiIno thnissb. o oIkh avaet tempttoge idv thee reader ag limposfem anyi nteresting apTphleisacepa ptliiocnasrt.ai nognfreso m theoretical appli cations-sauscthh e u seo fl ineaarl gebirnda i fferential equations, diffearnedn ce equations, leassqtu areasn alysesm-atnoyp racticaaplp licaitnifi oenlsds su cash archaeologdye,m og raphey,l ectriecnagli neeritrnafgfi,ca nalysfriasc,t gale ometryr,e latiavnidth yi,s t.oA rlyl sucdhi scussarieos nesl f-contTahienrseehd o.u bleds omethihnegre itnot ereevsetr yoIn e! havtrei etdo i nvolthveer eadienrt haep plicabtyiu osnisne gx ercitsheaestx tethnedd iscus siongsi venS.t udehnatvste o b etr ainedi nt heart ofa pplyimnagt hematWihcesr.eb etter thani nth el ineaarl gebcroau rswei,thi twse alothf a pplications? Timie sa lwayacs h allewnhgeent eachiIntbg e.c omeism porttaon ttt ahpao tu t-of-class timaes m ucha sp ossibAl geo.o dw ayt od ot hiissw itghr oup applpircoajtieocTnth se. instrucctaonsr e letchto saep plicatthiaoatnr soe fm ositn terteots htec lass. TheF loowfM aterial Thisb ookc ontamianthse matiwcisthi ntereasptpilnigc aitnitoengsra itnetdto h mea inb ody oft htee xMty. a pproacthod eivse ltohpme a thematificrssa tn d tphreonv itdheae p plication. Ib eliethvaetth ism akesfo rth ec learestte xptr esentaHtoiwoenv.e sro,m ei nstructomrasy prefetrol ooahke adw itthhe c latsosa na pplicaatniduo snei tt om otivattheem athematics. Historicalmlayt,h emathiacsds e velotpherdo uignht erplwaiytha pplicatFiooren xsa.m ple, thea nalyosfit sh el ong-tbeerhma vioofar M arkocvh aimno defolr a nalyzpionpgu lation movemenbte tweUe.nS c.i tiaensd subcuarnbb esu setdo m otivaetieg envaalnudee si gen vectoTrhsi.ts yp eo fa pproaccahnb ev eriyn structibvuets h ounlodtb eo verdone. Chapt1e rL ineEaqru atiaonndsV edorTsh ere adeirs l efrd om solvisnygs teomfst wo lineearq uatitoosn osl ving gseynsetreaThmles .G auss-Jomredtahno odffo rwarde limina tioinsu sed-iista c leaunn,c omplicated foarlt ghoserim tahlsmly steemnsc ounte(rTheed . Gausmse thodth atu sefosr warde liminattoari roinv aet th ee chelfoormn, andt hebna csku b stituttoig oetnth ree duceecdh elfoonr mc,a nb ee asisluyb stitiufpt reedfe rrebda,s eodn t he discussiinSo enc ti7o n.T 1h.ee xampltehse inn fa ctb ecomues efeuxle rcifosrec sh ecking masteorfyt hmee thod.S)o lutiionmn asn yv ariablleesat dot hvee ctsoprac eR n.C oncepts ofl ineianrd ependebnacseia,sn ,dd imensiaroedn i scussTehedy.ar ei llustrwaittehdti hne XVIII Preface frameworokfs ubspaocfes so lutitoosn pse cihfiocm ogenesoyusst eImh sa.v triee dt om ake thiasni nformailn troducttioto hne sied eawsh,i cwhi lble fo lloweidnC hapt4e bry a m ore in-dedpitshc ussThieo sni.g nificoafnt chee sceo ncepttots h lea rpgiec tuwrielt lh ebne a ppar entr igfrhotm theo utsEexte.r ciasteth si ss tagree quiarb er ieexfp lanation isnivmolving plvee ctoTrhse.a imi st og etth set udetnotu sn derstthaeni dd eawsi thouhta vintgoa ttempt itth rougahh azoef ar ithmetiIcnt. h foel lowisnegc tiothnesc ,o urthseen b ecomeans a tural, beautibfuuill doufip d eaTsh.ed opt rodulceta dtsot hceo ncepotfas n glvee,c tmoarg nitude, distanacnedg, e ometorfRy n .( Thisse ctioonthn e d otp roduccatnb ed eferretdo j usbte fore Secti4o.n6 w,h icihs o no rthonorvmeaclt oirfsd ,e sireTdh.ec) h apter clostehsr eew ith optioanpapll icatFiiotntsia.pn ogl ynomoifad le grne e 1t on datpao inltesa dtsoa s ys - temo fl ineearq uatitohnasht a sa u niquseo lutiTohnea. n alysoefes l ectrniectawlo raknsd tafrficfl owg ivrei steos ystetmhsa hta vuen iquseo lutiaonndms a nys olutioTnhse.m odel fort raffiflco wi ss imiltaotr h aotfe lectrinceatlw orbkusth, a sfe werr estrictlieoandsi,tn og morefr eedoamn dt humsa nys olutiionpn lsa coefa u niquseo lution. Chapt2e rM atricaensdL ineTarra nsformatMiaotrnisc weesr eu seidn t hefi rscth ap tetro h andlsey steomfse quatioTnhsi.as p plicamtoitoinv attheeas l gebrdaeivce lopment oft hthee oroyf matriintc heiscsh aptAe bre.a utiafuplp licaotfi omna triinac recsh aeology thaitl lustrtahtuees se fulnoefms astr imxu ltiplictraatnisopno,as ned,s ymmetrimca trices, isi ncludientd h icsh apteTrh.er eadcearn a nticipfoartp eh,y sirceaals ownhsy,t hep rod ucotf a m atrainxd i ttrsa nspohsaest ob es ymmetraincdc ant hearnr ivaet t hree sumlatt h ematicaTlhliyis.sm athemataitic tsbs e sAt !d erivaotfit ohnge e nerraels utlhtat th see otf solutitooan h so mogeneosuyss teomf lienqeuara tifoornmss a s ubspabcuei lodnst hdei s cussioofns pecisfiycs teimnsC hapt1e.rA discussoifdo inl atiroenflse,c tiaonndrs o,t a tiolnesa dtsom atrixtr ansformatainodna sne arliyn troducotfli ionnetr aarn sformatoino ns Rn.M atrirxe presentoaftl iionnetrsaa rn sformatiwointrshe spetcost t andabrads eosfR n are deriveadn da ppliAe sde.l f-contialilnuesdtr aotfti hoern o loef l inetarra nsformations inc omputgerra phiiscp sr esenTtheedc .h aptcelro sweist thh reoep tional soenca tpipolnis catiotnhsas th oulhda vber oaadp pealT.h eL eontiIenfp ut-OuMtopduetil n E conomiicss usetdo a nalythzeei nterdepenodfie nndcues tries. L(eWoanstsriieelcfye iavN eodb ePrli ze in1 97fo3r h iwso rki nt hiarse a.A) M arkovc hainm odeilsu seidn d emographyg eannedt icsa,n dd igraparhesu seidn c ommunicaatnidos no ciolIongsytr.u ctwohrocs a nnfiottt hese sectiionntsto h efoirrm acll asscsh eduslheo uelndc ourraegaed etrobs r owsteh routghhe m. Alld iscussairosene sl f-contTahiensesede .c ticoannsb eg iveanso ut-of-pcrloajsesoc rt s asr eadiansgs ignments. Chapt3e rD eterminanatnsdE igenvedDoertse rminaanndtt sh epirro perarteii enst ro duceadsq uickalnydp ainleasssp loys sibSloem.ep rooarfesi ncludfoertd h sea koef c om pletenebustsc ,a nb es kippiefdt hei nstruscotd oers ireTsh.ec haptcelro sweist h an introducttoei iogne nvaleuiegse,n vecatnodre si,g enspaTcheess t.u dewnitls le ea pplica tioinnsd emograpahnydw eathperre dicatnidoa nd iscussoifto hnLe e slMioed euls efodr predicbtirthisng a ndd eatohfsa nimalTsh.ei mportaonfce ei genvatlout ehsei mplemen tatioofnG oogliesd iscussSeodm.ei nstrucmtaoyrw si sht od iscudsisa gonalizoaft ion matrifrcoesm Secti5o.n3a t t hitsi me. Chapt4e rG enerVaeld oSrp aceTsh es tructuorfte h ea bstrvaecctt sopra ciesb aseodn thaotfR n.T hec oncepotfss u bspalcien,e dare pendenbcaes,ia sn,dd imensiaroend efined rigoroaunsdlar ye e xtendteosd p acoefsm atriacnedsf unctiTohness .e ctioonrn a nbkr ings togetmhaenry o ft heea rlcioenrc epTthser. e adweirl sle et hamta triixn verdseet,e rminant, ranka,n du niquenoefss so lutiaorneas l rle latTehdi.cs h aptienrc ludanei sn troducttioo n project--i-oonntsoon ea ndm anyd imensiosnpaalc eAs d.i scussoiflo inn etraarn sforma- Preface XIX tiocnos mplettheeesa rliinetrro ductTiopoinc.ss u cahs k ernelr,a ngaen,d t hrea nk/nullity theoraermpe r esenLtiende.ta rra nsformatikoenrnse,la ,n dr angaer ues etdo g ivteh ree ader ag eometrpiiccatlu orfte h es etosfs olutitoosn yss teomfsl ineeaqru atiboontsh,ho moge neouasn dn onhomogeneous. Chapt5e rC oordinRaetper esentaTthiero enasd weirl sle et haetv erfiyn itdei mensional vectsopra ciesi somorphtioRc n .T hiism plitheaste versyu cvhe ctsopra cies i,n a m athe maticsaeln s"et,h sea mea s"Rn .T hesies omorphisarmeds e finebdy th eb aseosfth es pace. Differebnats easl sloe atdo d ifferemnattri xr epresentoaftl iionnetsar ra nsformTahtei on. centrraoll oefe igenvaalnudee si genvecint fionrdsi ng diargeopnraels entiasdt iisocnuss sed. Thestee chniqaureeus s etdo a rrivaett hen ormamlo deosf o scillastyisntge ms. Chapt6e rI nnePrr oduSdp aceTsh ea xiomosfi nneprr oducatrsep resenatneddi nner producatrseu se(da wsa sth e dotp roduecatr liineR rn )t od efinneo rmosf v ectors, angles between veacntddo irsst,a nicnge esn eral vectoTrh esspiead ceeaassr. eu setdo a pproxi matfuen ctiobnysp olynomiTahleis m.p ortaonfcs euc ahp proximattoic oonmsp utseorft waries d iscussIce odu.l ndo tr esiisntc ludaid nigs cussoiftho enu seo fv ectsopra cteh eory tod eteecrrto risn c odesT.h eH ammincgo dew,h oseel emenatrsev ectoorvse ar fi nite fieldi,si ntroduTcheedr .e adiesar l sion troducteond o n-Eucligdeeoamner tyl,e aditnoag self-contdaiisnceuds soifto hnse p eciraell atimvoidteyol f s pace-tiHmaev.i ndge veloped theg enerianln eprr oduscpta cthee, r eadfienrd st hatth frea meworiksn ota pproprfoira te thmea thematidceaslc ripotfsi poanc e-tiTmheep .o sitdievfien iatxei oimsd iscardoepde,n ingu pth e doofirr sfotr t hpes eudion neprr oduthcatti su seidn s peciraell atiavnidlt ayt,e r foro net hadte scribgersa viitngy e nerraell atiIvtiit say p.p ropraitat theit si mteo d iscuss thei mportaonfcfi er smta stersitnagn damradth ematisctarlu ctusruecashs, i nneprr oduct spaceasn,dth ent oi ndicthaattme a thematirceasle aorfcthei nn volcvheasn gitnhgae x ioms ofs ucsht andasrtrdu cturTehsec. h aptcelro sweist ahd iscussoifto hneu seo fa p seudoin versteod etermilneea ssqtu arceusr vfeosgr i vedna ta. Chapter7 NumericMaelt hodTsh icsh aptoenrn umerimceatlh odissi mporttaont th e practitoifolnienrea alrg ebirnta o dayc'osm putienngv ironmIeh natv.ie n cludGeadu ssian eliminatLiUo dne,c omposiatnidoth ne, J acoabnid G auss-Seiitdeerla mteitvheo dTsh.e meriotfst hev arioumse thodsfo rs olvilnign esayrs teamrsde i scussIenad d.d ittiood ni s cussithnegs tandatrodp iocfsr ound-eorrffo rp,i votianngds, c aliInfe gl,ti ti mportaanndt welwli thitnh es copoef t hec ourtsoei ntrodutcheec onceopfti ll-conditIti iosnv ienrgy. interesttori enturng t os omeo ft hsey steomfse quatithoanths a varies ene arliienrt hceo urse andfi ndo uth owd ependathbels eo lutiaorneTs!h em atrixo fc oefficieonfta ls e assqtu ares problefomr, e xampliesv, e royft ena V andermonmdaetr ixl,e aditnoag n i ll-conditioned systeTmh.ec haptceorn cluwdiethsa ni teramteitvheo fodr fi ndindgo minaenitg envalues ande igenvecTthoirdssi .s cusslieoandv se rnya turailnltayod iscussoifto enc hniquuseesd byg eographteomr esa sutrhere e lataicvcee ssiboifnl oidteyis na n etworTkh.ec onnectiv itoyf t her oande twoorfkC ubai sfo undT.h ec haptcelro sweist ahd iscussoifSo inn gular ValuDee compositTihoinis.s m orec ompletthea tnh ed iscussuisouna lgliyv einni ntro ductolriyn eaalrg ebbroao ks. Chapt8e rL ineParro grammiTnhgifi sn aclh aptgeirv etsh set udeanb tr iienft roduction tot hied eaosfl ineparro grammiTnhgefi. e ldd,e velobpyeG de orgDea ntzaingd h iass so ciataetts h eU .SD.e partmoefnth te A irF orcien1 947i,sn oww ideluys eidn i ndusatryn d hasi tfosu ndatiionln i neaalrg ebrPar.o bleamrsed e scribbyes dy steomfsl ineianre qual itieTsh.er eadseere hso ws malsly stecmasn b es olvienda geometrmiacnanle bru,t t hat larges ysteamrses olvuesdi nrgo wo peratioonmn ast ricuessi ntgh es implaelxg orithm. xx Preface ����-����!���!��--------------------------------------------------------------------------- • Eachs ectiboeng iwnist ahm otivatiinntrgo ductwihoinc,th i etsh em ateritaolp revi ousllye arnedt opics. • Thep acoef t heb ookg raduailnlcyr easAesst .h es tudemnatt urmeast hematically, thee xplanatgiroandsu ablelcyo mmeo res ophisticated. • Notatiioscn a refudlelvye lopIetdi .si mporttahnatnt o tataitot nh ilse vebles tan dardb,u tt heriess omefl exibilGiotoydn. o tathieolnp usn derstanpdoionnrgo ;t a tiocnl outdhsep icture. • Mucha ttenthiaosbn e egni vetnot hel ayoouftt het extR.e adabiilsiv tiyt al. • Manyc arefulelxyp laienxeadm plielsl ustrthaetc eo ncepts. • Theriesa na bundanocfee x erciIsneist.ei xaelr ciasreeus s ualolfay c omputational naturteh,eb ne commeo ret heoretiinflc aavlo r. • Manyb,u tn ota lle,x erciasreebs a seodn e xamples ignit vheetn e xItti. si mportant thastt udehnatvste h ema ximuomp portutnoid teyv elthoepi crr eataibviel ities. • Revieewx erciastte hsee ndo fe acchh apthearv bee ecna refulsleyl ecttoeg di vteh e studeannot v ervioefmw a terial ciontv hearcteh da pter. �-���-�!�����-------------------------------------------------------------------------------- • CompleStoel utiMoannsu alw,i thd etaisloeldu titooan lsel x ercises. • StudeSnotl utiMoannsu alw,i tcho mpleatnes wetross elecetxeedr cises. • MATLAB prografomrs th osew how isth oi ntegrMaAtTeL AB inttoh ec oursaer e availafrbolme w ww.stetson.edu/-gwilliam/mfiles.htm. • WebAssiognnl ihnoem eworakn da ssessmweintteh B ook. • TesBtank • PowerPoLienctt uOruet lines • ImagBeank Designaitnesdtr uctmoart'esr iaarlefos r q ualifiiends tructoornsl yF.o rm orei nformation ort or equeasctc esst hteosr ee sourcpelse,av sies wiwtw .jblearning.ocrco omn taycoutr accournetp resentJaotnie&vs eB .art letLte arning resertvheresi gthote valuaaltrlee quests. ��-�!!�-��!!!-��-��-�-�--------------------------------------------------------------------- Iti sa p leastuorae c knowletdhgehe e ltph amta det hibso okp ossibMlye d.e epetshta nks got om y frienDde nniKsl etzifnogsr h arihnigms a nyi nsigihnttsto h et eachinogfl inear algebAr sap.e citahla nktsom y colleaLgiuseCa o ultoefrS tetsUonni versfiothrye rc on versatoinoln isn eaalrg ebarnadh erc ollaboroants ioofnt wadreev elopmAe nntu.m beorf LisaM'-sfi leasp peairnt hMeA TLAB AppendiTxh.a nktsoJ aneBte eroyf t heU niversity ofR edlanfodrsc onstructciovmem entosnm y bookosv earp erioofdm anyy earsT.h anks toG loriCah ilodfR olliCnosl lefogre v aluabaldev icoent heb ookI.a m mostg ratetfou l IvaSnt erlainndhg i sst udeanttS stM .a ry'Cso lleMgaer,y lanfdov,ra luafebeldeb acfrko m coursuessi ntgh eb ookI.a m gratetfuolM ichaBerla ntoEnr,i cFhr iedmaMna,r giHea le, WilMli leasn,d H arPlu lapaokfaS tetson Unifovret rhsedi itsyc ussainodns su ggestions thatm adet hiasb ettbeoro k. My deept hankgso est oA my RoseD,i rectoofPr r oductioofJn o,n e&s Bartlett Learningw hoo verstahwpe r oductoifto hni s bionso ukc ahn e fficiepnatt,i eanntdu, n der-
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