Linear Algebra: An Introduction to Abstract Mathematics

258 Pages·1993·5.73 MB·English

by  Robert J. Valenza (auth.)

UndergraTdeuxattisenM athematics
Editors
S.A xler
F.W.G ehring
K.AR.i bet
SpringSecri ence+BusMiendeisas, LLC
RobeJr.Vt a lenza
LineAalrg ebra
AnI ntrodutcot ion
AbstrMaactth ematics
Springer
RoberJt.V alenza
DepartmeonfMt a thematics
ClaremoMnctK ennaC ollege
ClaremoCnAt ,9 1711
USA
EditorBioaalr d
S.A xler F.W.G ehring K.A.R ibet
MathematDiecpsa rtment MathematDiecpsa rtmentM athematDiecpsa rtment
SanF ranciSstcaot e EasHta ll UniversoiftC ya lifornia
University UniversoiftM yic higan atB erkeley
SanF rancisCcAo 9, 4132A nnA rborM,I 48109 BerkelCeAy ,9 4720-3840
USA USA USA
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ISBN9 78-1-4612-6940-3 ISBN9 78-1-4612-0(9e0B1o-o0k )
DOl 10.1007/978-1-4612-0901-0
1.A lgebrLaisn,e aIr.. Title. II. Series.
QA184.V351 993 93-26143
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ISBN9 78-1-4612-6940-3 SPIN 10706145
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Preface
Theslee ctnuorteew sh,i ctho oskh afrpoem a o ne-semceosutrtesareu gthot
sophomaonrjdeu sn iaotCr lsa reMmcoKnetn Cnoal lecgoen,s tais tuubtset an­
tiaalb,s tirnatcrto dtuocl tiinoeanal rg ebArlat.h owuegu hs mea terfrioaml
elementary ocnoa clccaustlioiuo lsnl usmtarjaiotdree t ahse,ar reve i rtunaol ly
formparle requTihsiiissnt oettsos . a tyh atthm ea teirsie aalsM ya.n syt udents
whoh avnee vneere dteomd a kmeu cehff oirnpt r evimoautsh emcaotuircsse s
will tfihnemds eslevreisoc uhsallyl enged.
Whaits t hnea tuorfle i neaalrg ebOrnaem? i ghgti vtew oa ntipaondda l
complemernetpalryli iekwsea; v aen dp artpihcylseib costi,hl lumitnhaet e
truth:
THES TRUCTURERPALLY L.i neaalrg eibsrt ah set uodfyv ector
spacaensdl inetarra nsforAm avteicotsnopsra. ic sea structure
whicahb straancdgt esn eracleirztefasai mni lnioatrio ofnb so th
geomeatnrdya lgebAr lai.n etarra nsforimsaa tfuinocnt ion
betwveeecnt sopra ctehsap tr eseervleesm eonftt hsis st rucItnu re.
somsee nsteh,id si sciapllliounwsets oi mposrotm leo ng-familiar
andwe luln dersitdoeooafdgs e omeitnryts oe ttwihnigcashr n eo t
geomeitnar nioycb viwoauys.
THEC OMPUTATIREOPNLAYLL.i neaalrg eibstr hase t uodfyl inear
systaenmdsi, np artiocfuc learrtt,ae icnh nioqfmu aetsr ix algebra
thaatr iisnec onnecwtiitoshnu cshy steTmhsea. i mosf t he
disciaprlleia nreg ceolmyp utatainodtn hacelo ,m putaatrieo ns
indeceodm plex.
Thitse lxeta hnesa veivleydn,o gmatitcoawlatlrhysde,t ructruerpaIllnym .y
experiienbn octeh apnuadrp ep lmiaetdh emathteri eccso,g ntihtaaigt oi nv en
probslpeamic saev ecstoprai csoe ft einni tsoefml ofr vea ltuheaa nny a ssoci­
atecdo mputation. Morceoomvpeurt,a ptrrioeobanlalaelirm seast l imco st
exclusdiovnbeeylc yo mpuatnetdrh ,e reifnocreesh saanndt- driinml altirnigx
techniiqsbu oetrshe dunadnamdna tl adroitl.i nFaeilangrae lablsary ba,s tract,
noncomputationailso ftmeoannt ehfi'ersmse atnt ciocuswn ittmehar t hematics
asu ndersatnoadop dp recbiyma attehde matIih coiptaehn atsth.s e t udweinltl
leahrenrt eh caat lculiasnt eiiottnhh eperr incmiopdanelo,t rh per incgiopaall,
notrh per incjioopyfma alt hematics.
Preface
viii
Througwheoe umtp,h asstirzuec atnucdro en coevpectra lculTahteli eocn­.
turweirln lo tteh atth fier stth rcehea ptbeeratsrh nea meosffu ndamental
categHoerriaeer sseo. mfuer theexra mples:
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elegparnotoo ftf h ceh anogfbe a sfiosr mula.
(iTihie)p rooofft haes socilaatwfi ovmrea trmiuxl tipliispc oasttipoonn ed
untaftielrt hree preseonflt iantteiraoarnn sforbmyma attiroiincsise n st ro­
duceAdtt. h ipso iintbt e comseism palnay s peocftt h aes socioaft ivity
composoiffut nicotni ons.
(iTvh)e e quaolfit tyh ceo luamnnd rroawno kfsa m atriisdx e monstrated
entitrherloytu hgfeho rmparlo peorftt ihdeeus a slp acAec.c ordiwneg ly,
definteht er ansnpoojtsu esf tom ra tribcueftso a,rr bitlrianretyar ra ns­
formatainowdne fus l,l rye contchietlsweeno o tions.
Ano utloiftn heee x posfiotliloonw s.
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metrgirco ounp lettTehrimssa. t eriisoa,fcl o urusseel,da tientr h dei scus­
n
sioonfd etermiannladen atgdsrs a ceifunlttlohyne e xmto,rr ea ditcoapli c.
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nonstafnadrfaeora rdc ourisnle i naelagre bburttah ,re a tiofnotarhl eeii nr­
clushieorines p ,e rhiarposn iacsam lulcyph,e dagoagsmi actahle maOtni cal.
thmea themastiidacev a,el c tsoprai csfie r satna ddigtriovueap n,da l inear
transfoirsmfi artsaith o onm omorpohfai dsdmi tive grougprso.u pM oreover,
theoprlyaa yc sr itriocliaenml a trtihxe oTrhyu.ws e l atyh feo undahteiroen s
fomro sotfw hafto llaonwdws h,a fto lliosmw asd sei mptlheerr. 1e Obnyt he
pedagosgiidocena,mel u srte cogtnhiatzthec e o mpreheannscdio omnp osition
ofp rooifsts hc ee ntmreaalnb syw hiocnhee n compaabssstecrsoa ncct.e T phtes
grouipna, lo lfi tasx iomaautsitcep rriotyv,ia w doensd erful gtrroaufinondri ng
dealwiintgih n foramxailo maticT hsesy tsutdeweminslat.ltfi rslta cikn tui-
1
Wed on otv entubreey ontdh awth icihs m athematipcraelrleyq utiost ihtere e maindofet rh e
texfto;er x amplteh,eb asicco untitnhge orefmosfir n itger oupasr neo ti ncluded.