JoHhponksSi tniuseidt snh Meta hemlS acteiisec nac ianos csiwaitttihDhoee rn tp maeoMfnta th elmS acntic,iee csa ThJeo HhonpsUk ineivrnyss i t Matrix Computations ForutEhd tiion GenHe.G olub DepaorCfto mpmteueSnrct ei enc StnrafoUdin vye rsit CharFl.Ve ansL ona DetpmaeorCnfo tpm uStceeir e nc CoerUlninlv ye rsit ThJeo HhonpsUk ineivrnyPss eri sts Baltimore 1983,1 9192960T8,1h9 3Je, o hHnosp kUinenirsvsP irteys s Alrli grhetsseP ruvibesldh2.e0 d1 3 © Priintnth eUedni tSetda otAfem se roinac cai dp-afrpeeer 9 8 7 62514 3 Fisetrd i1t89i3o n Seceodnid1t 89i9o n Thdie rdi1t99i6o n Fouerdtiht ion 2013 ThJeo shH nopkUinenirsvsP irteys s 27N1o5r th SCthraerelte s BaltMiamroyr2le1a,-2n 41d38 63 wwpwr..ehjsuds.ue LiborCfao rnyg CroensNtsumr bole2 r02:19 43449 ISB1N39 :71 8--144-207h9e4-4 ISB1N01 :-1 4-472094h-e9 () ISB1N39 :71 8--14-42085e9b-0 () ISB1N01 :-1 4-42085e9b-7 () () A carteaclfooortrg hd i si asbv loaaoifrbkol me BtrhiLeti iabsrrhy. MATLAiBas®r e gitsrtadeeromeTfadh r Meka thwIonrck.s Spceidails csoa urena tvailfoabrbu llpeku rcsho afts hebiso oFko.rm orei nofrmaitonp,l ease coanctStp ceiSaall aet4s 1-0561-69o3rs6 p ceialspareslseh.su.j@deu. ThJeo hHnosp kUinenirsvsP irteuyss esen sv irofrnimeebnnodtmolakayl t leyir nicallusd,i ng recytceplxaetpdt e hriac sto mpooafst e d3l 0pe easrtpc oesntt- cwoasntwsehu,em neerv er possible. To ALSTOSN. H OUSEHOLDER AND JAMEHS. W ILKINSON Contents Perfea cxi GolblRa eefrceensx iii OtrhB eookxsv UsueUlfR sL xix CommoNnto ation xxi 1 MatriMxut liipclation 1 1.1 BaAsolitrgchi amnsNd ot tiao2n 1.2 Sttreuua rcnEdfc fiyie n1c4 1.3 BlMoacrctkiea snA dol rghimts2 2 1.4 FaMsati-t xVrePcortudtocsr 3 3 1.5 VercitzoaanLtdoili cotany4 3 1.6 PaalrlMetalr Miutxlii cpalt49i on 2 MatriAxn asliys 63 2.1 BaIsdifecra Lonsime A aelrbg r6a4 2.2 VecNtoorrm6 s8 2.3 MtarNioxr m7s1 2.4 ThSei nVglauuDlceeoa pmro si7t6i on 2.5 SbuspMateicrces 8 1 2.6 ThSee vnisotiSfyutq e aiS rymsst e87 2.7 FiitPneerc iMstairCoiopnxum tat9i3o ns 3 GenrelaL ineSaytrse ms 105 ---- 3.l TiranSgyumslsta e1r06 3.2 ThLeUF c artoiza1t1i1o n 3.3 RuodnfoEfor irrGn ua isasEnln iamtii1o22n 3.4 Pvitoin1g2 5 3.5 IpmvrioannEgdsm taitAicuancrycg 137 3.6 PraallLeUl 144 4 SpceiaLnlie aSrys tmes 153 --------------- ---- ---------------- 4.1 DioanDgaoilmnn caadenS ymmteyr 154 4.2 PsoieDt eintfviSeiy msst e159 VII viii CONTENTS 4.3 BadnS dyemsst e176 4.4 SymtmrIeienncfdti iSey msst e168 4.5 BlToircdokin Saatyglse ms19 6 4.6 VnaderSmyomsnstd e2e03 4.7 ClscailaMs tehfooTderosip Stlyzms st e208 4.8 Ccilurtaa nnDsdiec trPeo iSsysmsostn e2 19 5 OrthogaolnaitziaonndL eaSsqt ueasr 233 5.1 HuoeshoalnGdvdiee Trnrn sfoasr mati23o4n s 5.2 ThQeRF acztaotri2io46n 5.3 ThFelu- alRnLket Sa uqseaPsror ble2m60 5.4 OtOhterghroo nFacalrt oizat27i4o ns 5.5 ThReak Dn-feicLietSea uqnseatPsr or ble2m88 5.6 Sqeua danU rdnertrdenmeeiSdym sst e298 6 ModifiLeeda Ssqtu easrP robleamnsdM ethods 303 6.1 WeitgihandnRg e lgiauzrat3i0o4 n 6.2 CotniresnadL etSa qseusa 3r13 6.3 TtoaLlesS atq eusa 3r20 6.4 SbusepC aopcmutwaitttihShoeV n Ds3 27 6.5 UdpatMitanrFgicat xzo artii3o3n4 s 7 UnsymmetriEci gelnuvPearo blems 347 7.1 Porptesiar denD eocpmoisoint3s4 8 7.2 PterurbaTthoieroy3n 5 7 7.3 PowIetre ra3t65i ons 7.4 These snHgbea enRrdelS a cuFhro rm3s76 7.5 ThPeart caiQlcRA olirgmt h385 7.6 IvnraiSabunstpC aopcmtuea ti3o9n4 s 7.7 ThGee nlieezdErg iaelnuPvoerab le4m05 7.8 Hatmoiinaalnn odud tcEP girelnuPvoerab le4m2s0 7.9 Pesusdpcoter4a2 6 8 SymmteriEci gelnuvPearo blems 439 8.1 Porptesiar enDdeo cmspioti4o40n s 8.2 PowIetaret rio4n50s 8.3 ThSeym mterQiRAcg l oimrt h458 8.4 MoeMr tehfoorTdi rsd oianPalorg ble4m6s7 8.5 JcaoMbteih o4d7s6 8.6 CopmuttihSneVg D 4 86 8.7 GeenlrieazEdg ielnuPvoerab lweiSmtysmhmt e ry 497 CONTNETS ix 9 FuntcioonfsM atreisc 513 --9-1. ----Eeing·l·--evuM ate---h----od51s4 -- - --- . -- ··-- - ·--- 92. ApoxpirtmiMaoent ho52d2s 9.3 ThMeta rEixnxpet onia5l30 9.4 The, S SuqeiaR gro,nao ntLdoo gfM taar i5x3 6 10 LargSepa sreE iegnvlauPero blems 545 ------ --- 101. ThSeym mterLinazccoP osrc es54s6 10.2L nazco,Qs uaartdeaur,n Adpp xrioamtio55n6 1.03 ParcatLlia zcnoPcosrc ureeds5 62 104. LragSaeps re FSmrVwaeDo rk5s71 10.5K yrvlM otehfoorUds sny mtmrePoirbcl e5m7s9 10.6J aic-oDboanavn Ridlede asdMtt ehod58s9 11 LargSepa rsLei neSaysret m Problems 597 ------- -· 11.lD rieMcteth o5d9s8 11.2T hCeal slsI iatcetario6n11s 1.13 ThCeoju ngGartaeMd teiheon6dt2 5 11.4O tKhyerlrMo evt ho63d9s 11.5P ercdtoiinionng6 50 1.16 ThMelu tFimrgwearoirdk6 7 0 12S peciTaopli cs 681 ·--·-- ---- --·· --- --- · --- --- --- -- --- 12.1 LnieSaytrse wmisDts ihap cleSmtetrnruuetc 681 12.2S trrueRcdnat-Pkour ble6m9s1 12.3K orencPkoreudtrcC opumtat7i0o7n s 12.4T neosUrfon lndsga idnC onttiroa7nc1s9 1.25 TneosDre ocpmsoitainIodtni esor na7s3t1 Idnxe 747