Linear Algebra: A Modern Introduction

721 Pages·2014·68.31 MB·English

by  David Poole

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Printientd h Uen itSetda toefAs m erica
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Deditctoahm teee mdoo fr y
PeHtielrwt hwooana s,n
exemmpaltahreym atician,
educaanctdio tr,iu zneint- a
vecietnvo serer nys e.
Contents
Pfraecev ii
Ttoe hI sntruxcvtioir
Ttoe hS tudxexniti i
Chapt1e r Vectors1
10. Inotudrcot:nThi eR aceGtmarea ck
1.1Th eG oemeatnrAdyl goeVfbce rtao r3s
12. LenagntAdhn gThleDe o:Pt or duc1t8
EpxlaotrViceotnao:nGr des o rmye t
32
13. LinaenPsdl an3e4s
EpxlaotrThieoC nrP:ors osd uct
48
WirtPijrneoThgce Ot r:i ogtfih DneoPs trd ouacntd P Crdrouocsts
49
14. Applica5t0i ons
ForVceec to5r0s
CahpRteevri e5w5
Chapt2e r SysteomfLs i neEaqru ation5s7
2.0I notudrcot:nTi rivi5a7li ty
2.1I ntrotdSousy ctteoimLfosi n nE euqaart io5n8s
2.2D rieMcett hfoorSd osl LviinnSegsya tre m6s4
WirtPijrneoAgcH tiy:so tGfoa ruEsilsmiiiaonnna t
82
EpxlaotriLeoiMsnyC s op:mue Ttrlo Mde
83
ParPtiivgao lt in
84
CotuiOnnepagrit oAnnIst no:rd utctoth ieo n
AnyasolAifgslo rhimts
85
23. SpnaniStneasgn Ldi nIenaderen pden8c8e
2.4A pplica9t9i ons
AlloocRfae tsioounr9 c9e s
BlaanCchimenigcE uaqalot nis1 01
NetwAonraikls y 1s20
ElecNtertiwcoar1l4k0 s
LinEeocanro Mmoidce ls17 0
FitnLeii nGeaamre s19 0
ViegtThnteGeo l:bP aolns gii tnsSityoem
121
2.5I terMaettdihfosvo rSe o lLviinnSegsya tre m1s42
CahpRteevri e1w43
iv
Cnotents
V
Chapt3e r Matrices1 36
3.0 InotudrcotnMi:at riiAcnce tsi o1n3 6
31. MatOrpeirxa ti1o3n8s
3.2M atArligxe b1r45a
3.3 TheI nrvsoeeafM atri13x6
3.4 TheL UFa ocrttiizoan10 8
3.5S buspBascaieDsmsi,e, no snai,nR da nk1 91
3.6 IntrotdLoui cnTtearianorsn fot rimoan2s1 1
VgineRtottbieoc:s
226
3.7A pplica2t3i0o ns
MarCkhoiavn s2 30
LinEeocanro Mmoidce ls2 35
PopulGarotwito2hn3 9
GraapnhDdsi gra2p14h s
ChpatReerv ie2w5 1
Chapt4e r EigenvaalnudEe isg envecto2r53s
4.0I notudrcotnAi:D ynamSiycsaotlnGe rmpa hs 253
41. IntrotdEoui cvgtaeilnaounnEed is g enve2c5t4o rs
4.2D teeirnman2t36s
WirtPijrneoWgch tiC:mca Fehi rst: ThDeee triMmnaatnrti?x or the
283
VgineLwteitCsea :rC roonldleM'sne ostdah tion
284
EpxlonrG:aem toeriAtioppcl tinicosoDfa e ertmisn ant
286
4.3 EiegnvaalnEudie vgsee cnotnfoX rn Ms at ric2e9s2
WirtPijrneoThgce Ht i:ys o tEfoi nrgvesa l3u10e
4.4 SiimlaarnDidigt aoyn ali3z10a tion
4.5I terMaettdihfosvor Ce o mpuEtieignnvga l3u11e s
4.6A ppliacnatdthP ieeo ornnro-sbF uerTsnh ieor3e2m5
MarCkhoav in3s2 5
PopulGarotwito3hn3 0
TheP eornro-bFuerThsne iore3m3 2
LinReeacru rRreelnact3ei3 o5n s
SsyteomLfsi near EDqiuffaetri3eo4nn0ts i al
DiestLceir nDeyanra Smsyitceaml3s 4 8
VgineRtaktniSenop:sgrT atemasnS dec iahgnr Ittnheeert n
356
ChpatReerv ie3w6 4
Chapt5e r Orthogonali3t6y6
5.0I notudrcotnSi:h adoonaWw asl l3 66
5.1O trhogoinIRn"a l3i6t8y
5.2O trhogCoonmapll eamnOedtrn htosgP oorenjcoatnlis 3 78
5.3Th eG rma-cShimdPotrc aensdsQ tRFha oecr ttiizoan3 88
EpxlaotriThoeMn osed:Qid RFfi arcaittzoion
396
ApprmotaxiEininggv esaw litutehQeh RA g lroimt h
398
5.4O trhogDoignaoanla loiSfzmy amteitMoratnir ci c4e0s0
5.5A pplica4t0i8o ns
QuadrFaotrimc4s 0 8
GarhpiQnugra adEtuqiact io4n1s5
ChpatReerv ie4w2 5
Cotnents
Vi
Chapt6e r VectSopra ces 427
6.0I notudrcotnFi:i boin(naV ceccSitp oarc4)e2 7
61. VecStpoarac nSedbus sa pces4 29
WirtPirnoThgje Re icosVftcee :t S oapcre s
443
6.2L inIenaderen pdeBnacsaeinD,sdmi , e nosn i443
EpxlonrM:aa gtSiiqecous a r
460
6.3C hnagoeBf sa is4 63
6.4L inTearanrs fotrimoan4s7 2
6.5Th eK erannRedal n ogafLe i nTeraarn sform4a18 tion
6.6Th eM atorafiL xi nTeraarn sform4a9t7i on
EpxlonrTi:anl tgiLsiai,otc atentsdhC,y ers l tlapochgR irerasitct5i1o5 n
6.7A pplica5t1i8o ns
HomgoenLeoirunD sei afferEeqnutaitai5lo1 n8s
ChpatReerv ie5w2 7
Chapt7e r DistaanncdeA pproximati5o2n9
7.0I notudrcotnTi:a xGioecmaebt r5y2 9
71. InnPoerudrc Stp ac5e13s
EpxlaotriVcoetnanosMdr:as t wrhiiC tcoemEsp nrlstie ex
543
GeeotmIreniqicuta ainlOedtps ii tzmiaPoorbnl ems
547
7.2N ormasnD dsi taFnucnec ti5o5n2s
7.3L eSauqsatrA pepsr oxim5a6t8i on
7.4Th eS niguVlaalDrueo ecm ptoisoin5 90
Vgint:eDe tigIimtaCagoplemr i eosns
607
7.5A pplica6t1i0o ns
ApproxoiFfmu antcitoi6no1 n0s
ChpatReerv ie6w1 8
Onloinnley
Chapt8e r Codes 620
81. CoVdceet or6s2 0
VgineThteCt oaedb:Sas yrt em
626
8.2E rorrC-orrCeocdtei6sn2 g7
8.3 DuaClo de6s3 2
8.4L inCeoadre 6s3 9
8.5Th eM iniDmsiutmao nafCc oed e6 44
APPEXN DAIM athemNaottiaactnMaidelo t ndh osoPf r oAolf
APPEXNBD IMatheImnadtouincc taBil 1
APPEXNCD ICompNlumebxe rCsl
APPEXNDD IPolmyilnaso D 1
APPEXN£D ITechnBoyltoeOgsyni lnoyen l
AnswteSolr eesc Otdedud-m NbeErxeiedsr ecAsN IS
IndeIxI
Preface
1he laosntke n towhwhisenw ngr itai ng
booiwksh attpo u fitr st.
-BlaPiassec al
Pens1e7es6,0
Thefo uretdhi otLfi ionng eeabArrM a oA:dIl enortdnru pcrtevisetoeshanr ep proach
anfdae tutrhueasstfoe urnstd bo e stortfeh pnerg etvehidsooi nutHssio. w eIhv aevre,
streatmhtleeis xnotem dea wdhdanetud,m ecrloaurosin afisnc,frda e tsihueptn heed
exceir.s es
Iw asntt udteosn elteis na elagareas bn er xac siutebicajntngt d ao prpetcieit as
treomueusns desfuAslt.tn h esea tmieIm w ea,tn hote tlhpe m tmhbaeas cstoie-ncr
cepatntdse chonlfii qnuaeelasgtr eh bartaw intlehliee ondyt hcueorrs beosit,nh
mathetmiaacnisdon t hdeicrsin pelIas il.ws aosn ttu dtaeopp nrtetsce i itanhtee rplay
otfh eorapepltiaiencnddau, lm ,e mratihceamlta httpa ievcrasdt ehsseue bcjt.
Thibso oidkse sifogrn eiudnas nie n troodnuoecrt-to wo-mrseyes ctoeurr se
sqeueinlnci ena elragarFer. ibsa tnfo dr emioitiss nt t,e fonrsd teutddsa en,Indh ave
trmiyeb sdett wo r itbeo sottokhh seat tu dneoontnt wlsiyfi l nlidr t e adbauabtll seo
wiwlaltn rot ei a.Atd s tihnet hfierrdesoietnt Ishi ,a vei ntatacokc eonu nt the reality
thsattu dents talkiinanelgag areir blnerit aktr eocol odymfru eoc matv oarroyif e ty
discsiI.pna l didnitetomi aotnh emmaajttoihrceesa sr,r a ept tob em ajfroorms
enginpehseyirccihsne,gm, ,ci osmtprsuyctieberin ocleeon,ogv nyim,re snctiaeln ce,
geohgyer,cao opmnipcssy,c ,hb ounlseoiasgnsyed,d ucaawste ialooslnt ,hs etru dents
taktihcneog u arassne e l eoctrtfuo il vfidele lg ree requgiltryhbe,eom oekn ts. Accordin
balatnhecaoenarsdpy p liicwsar tiiitanoct noesnn,v ersstyayeitlfutsiel o lnya lr igorous,
ancdo mbait nreasdp irtetisaoetnwniaicolton hn focres rtnu- decenntlteeraerdn ing.
Theeri nsos utchhai asnu gn ivbeerlssetaa lsrltnyIyi anlnn egcy. ls ta,hse we irll be
somset udwehwnoot rsk i nwdedeleplne atnnlodyt hwehrwoso rbkei sgntr osu;p
sowmhepo r elfeeecr-t ublraesaeardnn oidtn hwgeh rtosh riianwv oer kssehtotpi ng,
doienxgp olonsrsoa;wmt heio aelngjeombyar naiipcus loawmtheiao or aneds ea,pt t
numecrailccau(llw aiattnwihdio tnahsc o oumtrp ua)tn,sed o wmheo esxthriobnigt
geomienttruiIicntt hieiodsni .Itc ioonntt,iop n reuenemst a teirnavi aarloi fe ty
Fomro orne rtehceeo nmdmatiwaoynsasg- lebyrg,aem ioerctiyacn,lau lrlmilleclanayvd,e l yrl-sbtoah aatltyl op lfeaesr­ n
otfh Lei nAelagCreu brrrai cuelrusmfi ncdpat antha foo l lIho awav.le as tot etmpoper etsnettdht eh eocroemtpiuctaal­,
StuGdryos ue1hpee,C o glel e tioannaadpl p,tl oipieiandfc lse yxeiitnb tleewg arIy.adn to eisdnoi ig,tms yh oetp hat
MatehmtaiJcuosr na(l9 193als)lt u,dweib nleeltpx so stetodh m ea nyo lsfii ndaeelrasgar e. b
4-1462.4 Thibso iocsko mpwaitttihrhbee l ceo mmeotnfhd aet ALiliognnCeesuba rrrra i culum
StudyF rGoarpm oe gudopag.pi ocoiavfnli t te hwie,nsr od e o utbhfotarm t o ssttu dents
Vii
Preface
Viii
concerxeatmseph lopeursle dac besdter Iha actvtaeik toehnani.p s p rhoeaIrac elh.s o
belsitervtoehnl agitlna yel agirees bes rnslatla iyba ovuetca tnotdrhs sat tu dneetneotd s
sevee cfitro(nsri tcsa o ncsreetittoneir ntdggoe)a rs i ongm eeo mientsrMiiogcrh eto.v er,
introvdeucectaioarnrllgsly so twusdt eos nehteos sw y sotlfei mnsee qauraa triiosnes
natufrroaml lgye ometrict hpaerrneoi qbsulenae almtlsuay.rcs ao Mlealffitycr iiecnets
matorlfiicnseeysas artn eadmas sg eoncfth sa( nlgitenr eaantrsni foso.Thr) imas sets the
stfoarge ei genavnoedrc tthooprgrseoo cjntabiloo otnwfhsh ,ia crbhese u tn derstood
geomaelThtleryd i.atc rhtaa ptp oenta hrceso votefhr bi osso ykm baov leicaztneodsr
refmlyec cotnsv tihcgatetio omnue ntdreircss thaopnurdleidccn oegmd peu tational
techniques.
Ih atvreti loei dtm hinetu meobrtf h eoirtneh tmee.sF x ottrhm eo psratt ,l trse su
labaetslh eedoe rietwmhibsele rl luasitetnedh tr ee o xsrtu mmparreiczweeod rikn.g
Interreesstuthtalia rtnnesgoc te nltt torh baeo hoakbv eee n iaensxc relcuiodsree ds
exploon.Frs oaertx iamtphcleore sp,sr oodvufec ctit dsoi rssc ounsilsenyex dp lo­
rat(iniCo hnpast earn4sd )U 1n. l mioklseit n aelagtree bxrtatb hobiooskho sakn,s o
chaopndt eertrme inntThasee. es nstrieasalura lelit Slnsce t4io.wn2i ,ott hhi enrt er­
estmiantgec oraniitanilaen end x ploThreba otioihskoo, nw .ec voermrep,hv efoen rs i
ani ntrotde.uWx chttreoerpvyeob rsl sIhei a,iv nec leuldeemdea nnatdca cbrelyse s i
proootffsh eoironer mdtsaeo v rioh da vtisona "gyTh ,pe r ootofhf ri essi busyel otn d
thsoecep o tfh tie:sThx' et r esuIhl oetpa, w iostr,khti a ssle- foctnained.
Ih anvoebt e setniw nitgthyhae p polniThsce:ar temi aanmryoe ri tenh beo tohka n
cabnce o vears eidnc goiluHnero sweei.ivt es r i,m tphsoatrtut sdaeetnenhtit e ms p ressive
ranopgfre o btlwoeh milsci hna elagre bbareap pIclh aianeiv dne.c lsuodmmeoedd ern
matoenfir niliaitlnae el agaren bcdro adt ihnetgoh iransyton to rmfoaulnildny i natnr o­
ducltionraeyla gtree bThxretara. er a els seov iemrpavrlere esaoslria-lpwdp liocfa tions
linaelagre borniaet oeahfmni ds tionfro pitrc aaciltn,it cteahrlee,ss et ;a aprpel ications
presaessne tlefd- "cvoingtnaeitnteeds :'
Ih otpheia nts twriuelcnltj oorys fr toetmah bciohsoMi kon.rig em poIrh toapnet ,
thsattu duesnitnbsgo wotikchl oelma wewa iyat nah p preoctfih baeaet uiptooynw, e r,
antdr emeuntdioollfuii stna yel agaren btdrht aah twe iyhl alfuv nea lotnhwgea y.
Wha'tsN ewi nt hFeo urthE dition
Theo vesrrtaulcaltn usdrt oeyL fli e nAgeleabArrM a od:eI rndntu ircorotenm tahien
saimtneh foeu retdthii. o n
Heirases ummoawfrh yian ste w:
Thea pplitccodao ittnihgoe hnoasrbv yeem e onv tetodh eo nnleCiwhpn ate8e .r
• Tofu rtehnegra gtefis v,swe tr uipdtreieonnchjgta sbv eeae dnd tetodh e ex er­
ci•s seeTt ehssp.er e ocgjtissv teu dace hnattnsroc e ers cehaw raainbtdoea u stpo efc ts
Sepea ges
49, 28823,3, 0 14,4 3 thhei satnoddre oyvp emloelfnitna elragaTre.h bee xo parlotnivsi,gt neaesnmt,dan y
otfh aep plipcraotavidioddniemst a itoefonrrasi lta ulpdr eeoncjtt s.
Theera roev 2e0rn0 e wr eiovsree exdre csIi.nrs esspteoor n evicemow­ers'
me• ntthesie ,nsr o awfu lplr ootofhf Ce ua cShcyh-wIanruezaq liiCnth pyat 1ei rtn h e
foromaf g uiedxreecdi se.
Ih amvaed neue morussma lclh aniwgnoe rsd tioin mgp rocvlea orrtih tey
ac•r cauoctfyh e ex ptooinAs.li ssveoe,dr eatfilin hoianbvsee me andm eo erxep blyi cit
givtihnegm tdheetfiiinrboi onoxa wennasdf erwe shualbvteeshe ing hlbiyg hted
labtehleitmnh gea sos.r em
Alelx iasntciinhlgal bvaeerue ipned sa ted.
•
Preface
ix
Features
CleWarri ntgSi tvle
Thet eixwstr iitasst m eipnld ei,rc eocntv,e rssltaAeyts.i omanupsaco blhsl sIhei a,v e
us"emda tthieEcmnaagl"lr iaestrhhn rt ehlaeyxeicisnvsgoe nlm ya thelnm oaatt­ica
ti.Ho onweavlpelrrso ,t o htfaa rgei vaerfunel rliyog uoasrn,Ad pp nedxi cAno tains
ain ntrotdmoua tchtetimionacnoa tlafo trtoi hsownehw oi tssoht retahmoelwiinrn e
wriCtoirnnecget.xe a mapllmaeolssw ptar yestc heeedmoewsr h,ia crtheh fo elnl owed
byfu rtehxearm apnaldppe lsio cn.Thas itfsil ow-sfrpoemtc goi efincae nrbdaa lc k
ag-aiicsno nstti hsrtoeutnghbheoo oukt.
Kevc oncepItnst roduEcaerdl y
Mansyt udeennctodsui nffitcieulnrli tnayel agwreh bernca uo trmhsoeev fr eostm h e
comput(oasltvisioynnsgaot llfei mneseq auoranm tsai,pn uilavteicantngomd rat sr i­
cetsot) h teh eor(pesatninsciealntligs n ,ie nadre pesnbudsepnabccaeesa,sin ,sd ,
dimoen.nTh) sibiso ionkot druacloetlfsh k eec yno ceoplfti sna elagerera bliryana,
cnocrsteettibene gfor,re ev itshiietfunmil gnleg nl eiVrteaycc.t oonrcs euapcdstho s t
prodluecnotgr,tt hh,ot gya,onp ndrea olcojitnai rfierd sits ciuCnsh psate1eid rtn h e
2 3
cnocertsteet oiIRfna gn IRdb efotrhmeeo green neortaoilifo n npnsre ord nruocmt,,
anodr thopgreootcnjiaaoplenp a irCn h pat5ea rns7dS . i mliysla,pan rnsienatgns d
linienadre paerngedi evacne nocncee rtt eera ttim Cneh npat2ep irro trto h geeinre r­
aliztvaote icsotpnoai rcCn eh psat 6eT.rh fu en damlce onntcoaesfpu tbssb paascies,,
anddi moenan psepiafirri sCnth p at3ew rh etnhr eoc wo,ln ua,mn ndu slplao cafe s
maxta rriieno tdruciitens do u;tn Ctahiplt 6t ehtrta heisdaeera gesi vgeenrn aeal
teratmIenCn hptat.4e e,ri genavneadil gueensav rieenco ttdrouarcnsed d explored
for2 Xm a2t ricesX bceofoturenera ppptaaehrrBet.ytis hbr eg e inonCfih npag­
te4ra,lo ltf h keec yo ncone lfpin tnasel aghrea bbvreeaie nnot druwciectdoh,n crete,
computeaxtaimtopsonlu aeplstp hoerWmth. et nh iedsaeepa epsai rfun l gler naelity
laittneh breo oskt,u dheahnvatetds i mgee utts toeto d h eamnh de,n acrneeo,s t o
intimbiytd haetme.d
EmphasoinsV ectoarnsdG eometry
Ink eewpiittnhhgpe ih lostohlpaihtnya e lagriep sbir rmala ayrb iovueotcr ttsh,i s
bosotkr geesosmeiesnt torunAii.cct c ioyrt,dh fiiernc sghptlat ieasrb ovueotcr atsn,d
idte vemlaonpys ctohtwna icalepelppa rtrese tp aetdhlryo utghthee.oC x uottn cepts
suacoshr thotgyp,ore nocjatlaiinlodin n,ce oamrb ianraaelfot lui noidnCn h pat1e,r
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asa c iosrm ephveetne rsaittmo elfni annepdsl ainnIRe tsh parto veiesdnsetsi al
inigsihnttt hose o luotfsi yosnot lfei mnsee qauoran. Tts ihiesm phoanvs eiocsrt s,
geormyae,nt d vtiisiofousnua nltdih zraoutghthee.oL x uittnt eraarn tsifoaorrnmesa
inotdruacmsea dit txrr antsifoiorCnnmah satp e3wr,i thg omemaenetyxr ailmcep s,
befogrerena leli nteraarnt sifoaorrncmesoa vieCnrh epadt6 eI.rCn hpat4ee,ri gen­
valaurieenso t druwcie"tdieh g enpaisacv tiusraueiThasdle".p rooofPf eo rnr's
Theorigesim vfi erhnse tu rlilasyntt dhi foecrnaml yali,bn o ctahus seiasgn ego metric
argeun.Thmt eg eomoelfti rndyeya anmris cyaslrt eeimnsafo nrsdcu emsm atrhiez es
mateornei iagle navneadil vgueeoecnrs.Its nC ahpt5oe,rr t hopgreooconjtnaoislr, ­
thogcoopnmlaelmo esfbnu stpsaa nctdeh sem, - GcSrhamtPi ordcaersaespl rle ensted
itnh ceo ncstreteoitIRfne3b g e fobreeig negn ertIRoa" la inzdCe,hpd ati 7ent,r io n ner