Algebra lineare e primi elementi di Geometria

356 Pages·2011·26.08 MB·Italian

by  Maurizio Candilera

MauriziCoa ndilera
AlessandrBae rtapelle
Algelbirnae are
priemlie medniGt eio metria
e
McGraw-Hill

colladniia s truzsicoineen tifica
serdiime at meatica

MaurizCiaon dilera
AlessanBderrat apelle
Algebrlai neare
e primie lementdii G eometria
McGraw-Hill
New York San FranciscWoa shingtDo.nC . Auckland
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ISBN9:78 -88-836-6198-1
PrinitneI dt aly
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Indice
Prefazione VII
1 Vettorgie oem etruinaa,l ungian troduzione 1
1.V1et tgoeroim e.t r.i ci. . . . . . .1 . . . . . . . . . .
12. Stotosvpeatzteiod riipaelnlidi ernnee.z aa. .. . . 5
13. Prodsoactltaporr eo,dv oettttoo riamlsiet oe prod7o tto
14. Sapzaifnofie es paezuicol ideo 11
15. Isomeea tpprlizieic oaanffiin i . 18
16. E esricz.i . . . . . . . . . 1.9 .
2 Spazvie ttoreia aplpil icazliionneia ri 25
21. Grupaepnli,l, i corpi . 25
2.2Sa pzvie tto.r i.a li 26
2.A3p palziiconi. lineari 35
2.4Ma tr. ic.i . . . . . . 38
2.5Ma tarsicstioae cd aip palziicoanrii linea 41
2.L6o s pavzeitot dourai.la el e 45
2.7Ees ricz.i . . .. . . . 50
3 Sistedmiie quaziloinnie ari 59
3.S1lo uzdiios ntsieli miin eari 59
3.E2l iinmazdiGioau nses. . 61
3.D3e compoLsUdi uizn imaoa nter ice 67
3.E4es riczi 68
4 Determinanti
73
41. Apipczlaiomnuil tiallitnee.rna arn.it i. . . .7 3. . . . . .
4.2Es sitednfoizr amn e-i lneaalrtie: rnr aengdtoLiila ap lace 77
4.3De termdienfiannnieetaz eli:co purnoep .r ietà 80
4.4M in.or.i . . . .. . . . . . 86
4.5Ap pzliioeccn aoim plementi 87
4.6E ser.ci.z.i . ... . . . . 93
VI Inidce
5 Spaziaof fines pea zeiuoc lideo 97
51. Spzaaiffi ni. . . . 97
5.2Sto tovari.e tà. l.i neari 101
5.A3p pliacffianzi.i o.n.i 140
5.C4o ordbianraitcee ntriche 160
5.S5ap zeiuoc lideo 101
5.E6es ricz.i . . 191
6 Autovaleoa ruit ovettori 127
61. Endosmomerim fi atsriimcii.l i. . . 172
6.2Au tovgeetnteorreait l eiodzrJizioa art .di a n 133
6.A3l caupnlpeai zcioni 124
6.4Ee src.i zi. . .. ... ... .. .. . 151
.
7 Applicazbiiolniin eeai rsio metrie 161
7. 1A pplibcialzriisinoi enmaim eeta rlitceh.rne a nti 161
7 .F2o rqmueat dcirhae. . . . . . 176
7.C3l aszsiiodfinfoicer a mbei lrii.n ea 176
7.4Is toimree . . . . .. . . 127
. .
7 .T5r asforomratzoigoonnia li 147
7.M6o mveinrtiign iedlsilp oae zuicol ideo 177
7.F7o rhmeer mitiane 181
78. Eesricz.i . . . . . 178
A Numercio mpleesq suia ternioni 201
A1. Numecroims psl.ie. . . . 210
A.2Tr asfordmMiao zbiiounsi 205
A.3Po riezsitoenrece ao. g rafi 210
A.4Q utameioenr io tazioni 212
A.T5e ordeFimr ao benius 216
A.6Ees ricz.i .. ... . 217
B Conichnee llsop azeiuoc lideo 223
B1. Coniche 223
B2. Eser.c i.z i . . 228
e L'aneldleoip olinomi 231
C1. Pridmeefi niepz rioopnrii età 213
C.2Po liendeo nmdio smmoir fi 236
Soluzioni 241
Elencdoe is imboli 327
Indicaen alitico 331
Prefazione
Ler ipemtoudctihenfiel e 'lrodinadmeegnltiuo n sitvuecdrhisse isi to ansroui c ­
cednuletl'leuit mdoe cennipoo rhatva aantarnozi oi,t o anlivmoollrttiaol evanti,
nepir ogrdaecmiom rids ibi a dsiMe atemcaadt eilFlaec osilcetfinàhct eeit ec­
nlogoicrhliesev,ono dsqiu asseim ipnru enr ai dudzeicioo nnet enuti proposti o,
nle miigoldreeci a isnui n,ra e distdreigablruigz oimocenhnneeect soit ituivano
ls'soattudrraiaz lieo.n a
Snoos tpartoipq ruiecosma tbii amcehcnehit a in cnoors etatr tiip elnas are
presendtecaioz nitodenine uc utoniri snoli dezi iA albgrelai rneeeG aeometria
negolrirai rdiio cntu itidli o cestnirt oeaov pae rnaenriue oc voird lsiai u Lri'e­a.
deac hciagh uei èds attqaout eadl dila aur nei' ntrosduuiffizecinotneedm eetnttae­
gltiaaial A'gl eblrian seoaotrltein nd,eqo auapnodso sgilabisi pl"eeegt,ot miie ctir"
diq uetsetaoas,r i inlaee lm otiiovsnainizae lalplepai zciaolngliea o mdeetgrliai
spadzdii i mseinneofi int(ane o slno toir dimelnis)i.o na
Itlla igdo elpelresan taèzi inotnreo edd uitdtoai:btv etloniu cndga'ilse lesre
unt raetstuaasittvsolou' lragomevnutoplore,o pico ornrtepe eunrunp t riic moor so
(trimoes setmrreaascllteeer) c dafoinr dnoi raeu ,n paor letsreena tuatzoicoonne­
tenduetgaals ipg eetntleiiar n,ac mhoet iveadeze simopcnihis e p erpioasnmoso a
esseurteai c loirl oco haeff ronltmaaa ntoep relirpaa ir ma vOoglnctpiaai .t olo
èc olmeptadtauo 'na mpsieadr eiis ece irdzdiii ,f fivcaobrliitllaàcee u ,si o luzioni
sotnuort catlceeot a lfilnade ev lom leuG.le isrc eiozliat,p r eer meatllte etdrtieo re
veirfircielag raddcioo mpsrieodnneelm latae prrieas,ea vn otliatnnaedoz i icoo ni
proppoeasrpt per ofonndeilsmltdeouin ot.i
Peorr iemnetgailrll ieeo t dtioardmeiso, e guunidate os crpiipzùri ieoscnae
declo not deensiui tncgpaoiliti.o l
ICla ptiol1o d evesese croen esriacdtoomu e'ni ntroadudaz licfaoutnnteii
elemecrnictlaaga re io mdeetplrin iaoead elslpoat ziridoi melnecs,hi eo nfiano a
qualdcehceefa ne nriabone on nsottiu dceahingentl viiiaz niuonap ercuon­riso
versiItnao,rla ittort.er ia vevregsteoto omireceilti ler o prroo plrosit eutdàe,n te
vieanvev icailnnloaezt i"osoa rtnaitd tise p"a zio svoesttpzttaoiodori,ip aelne­,
denlziaanr, eee cecrecath,ve e rrsavninloun pecpipaa littsieouc cessQiuveois .t
capiptueoòssl eoir neil mzeinate ot raaffildaastcaoiu atato lonue ontmdataa u ra
pardtelleos tudIetlne tèsei t.no t egnruamteofir ugodrscaeeh i el rlauinsnot mo­
dop idùi rgeliat rtgoo emesnpetoi isll te itp tuocòro uemn qsuaegr gelip aar opria
comepnrnseid eocio ntternauumt'niaitm iepsa e dreiis ece irzi.
Lat rattvaezerp iaro oncpeor miai nsccuicaev sodCas apiitlo l2o i cnu i ven­
goneos peol sedt efiniez riiio snuil tatis ufolsnltdara udmteetgnsualtprizaa li i
vettdoidr iimieaonlfinsiine t esa u alplple iclaizniterotaanasr lipizi ai T.u tta la
VIII Perfzaione
disicouvnsiese snveos lut caua nma prob iatnrcashrgeeil e ois eemg pleiisr ecizi
vengpornoops ounsiut mire zariilo rinea,oa c loime pslAslic.au rngio mceonnt­i,
sidaev roalnttoiien n disbsaip,cle oinmgels ip avzeit tqoourizieanolt tieie oremi
diios mosrmfivoe,n gono sportfoetrsomde aein s tceairtzii .
Lat eodresiiia s dteieq muial ziinvoeinaesirnv ieos letpaa rantealm esnutce­
cessiCvapoi to3l,od ovvee ngdoensocl rtaie tctdneeii l ciam idnGiaa zueis osn e
alcsuunaepep l incia.z io
ICla ptiol4o p rseenltnaao zidodin eet erdmuii nen nadnotsmemoeo rl fie
super opdrainesdtpoàa a,zq iuoa lapcplhaiezc i.Do anlp eundtvioi gsetoam etrico
sèic erdcieant faot ilaz'ppzlaairzceid oendlee termaiclln acaondtleveoio lumi
negslpiav zeit troerdaidilai ilm siein noefi nita.
Neslu cscieCvaspoit ol5o s iin terlrtaor maptetd ae'Azllilgoenlbeir rnaee a
peirn troldgau erormede etlrsailpaoza iffinoee d elsalpoze icuol icdeeroc,an do
diil rlaursdeti vire arpsptior lradet u ie sgteroutmitecuthArrebe.b iraimtoe nuto
opporitnusneqoruq iiur aelc cehnaen'l oslu od elcloeo rbdairniahctecee,hn e t ric
srii velasnucolma purote iaplleiierll o lreomg eca olnpe r opdrciio enstvtsàeài
delslpioao z.
IClap itol6 op rseenlttaar attdaezflirolomecn eea nodneilmclaheted ri i ci
endosmmociro,fipn a rtirciogluaarfrreod mo a aldlieaaa lgflrooamn daaJi lo er ­
daAnl.l ad ecfilpan iet eon lenoiu mseeires ocriszoins oti altrela uvtsaetra ipe­
plziicoeacn oim plecmoemlnedat e ic osmiipozodnSieh c uor v ia lsoirnigo o lari
le'psonzeidnamila eti r.i c
NeClap ito7l so airff onltcaal aszsiiodfinecelaa plpel icbaiiznliesoaunrli i
camrpeoa( lece o mplmeossstor)al nrelde aoznieo lnfeiro mqceuo na der.a tich
Viednaest poa azq iuoa lacplhpaiezc ieog neeni ezrzaaliznitornoedg urcuepnpdio
dii soimeleca,tl raszsiiodfinemceioa viim erdnietglsilpdoaei zu idcoel, loi sot u­
didoe flrolmeh ee rimaeini tetl e osrepetametla.Ar n cihnqe u oec satpigtloil o
esceirozlita,r r aeff olrczaao rmeepn rnseid oelnloez iporneis epnetramteet,t ono
numearpoopsforin di.m enti
Let rApep endiscio,dn eod iacda taer gdoimveeep nrostssoiien ssoe urtei liz­
zaotm ee nnoe'a lmlbdiit ou snoL .A'c poprenAdr iicgeuin a urdmcaeo rmip lessi
e qiue anrtioconanit ,t enazgailsiop ngeeet otmcieei ct orpnia rtiecnofaslsuailr lee
trafosramzidoMino biie ul sgae omderite retic taee r ncephlaii n doGi a usPse.r
quarnitgou iqa urrnadtai eosnèiis ,ec ldtido arn eu npar esenetssaeznlizeoi,na e
mettieennv diod qeunaezssaic v laumseiinllto uert oi nliezlrzalpoap resentazione
delle rotaztiroindsiii mlodeenLena.a'lp lpoe snscdipoi ancdzceepil roue sentando
undai mroasztiotneeo drdFieer mlo ab cehmneoi sutsr air elcaiioc ,mo eml pessi
e qiu atesrnniioalo uenn ii aclhgeec bernets ruJR.a elais r seue nc orApnoc.h e
queasptpae ènc doircrede aud 'naatmaps icaed leits caei rzi.
LA'ppenBdo iffcrueenp ar esenatuatzoicoodnneetlc eloinencu nthepaeli a­
noe ucelori,id manadu ansn udcosc iecvsoor dsigo e ompertoriiea ttiva per una
trattpaiczùoi mopndleee'a lgtrloam e.n to
LA'ppenCdp irsceeenl tpear operlieemtedàne ptioa lriie n oqumlaiol rcoh e
aplpaizciaolnsleto u ddii eoun nd osmmodoriu fi nsop avzeitot doidr iimaelne­
siofinineti an,t rodlufarco emcnaad ona or naizcipoelnrmaa a lterd iuicn te a le
endosmmoor.fi
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