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Co ntents
f*i4?u'6f4 Chapter 1 SYSTEMS O F L1 SEAR EQ UATIO SS 11 .1 Solutlons and Elem entary O perdtlons 1
1 .Q Gaussldr l Elllnknatlon 1 01 .3 hlonlogeneous Equatlorls 24
1 .4 An Applfcatfon to Netvvork Flokv (O ptrond/) 271 .5 An Appllcation to Electrlcal Netkvorks (O ptlondl) 29
* ;4%%%:*$ Chapter Q M ATRIX A LG EBRA 33
Q.1 M atrlx Addltlon Scdidr M ultlpllfldtlon dnd Triinsposltlon 33Q.Q M dtrlx M ultlpllcatlon 43
2.3 M dtrlx Inverses 56Q.4 ELgrrlentary M atrlces 68
Q.5 Lu-Factorlzatlon (C ptlonal) 782.6 An App/lcdtlon to pnput .o tktptlt Econom lc A/tade'ls Lcp tlorîal) 902.7 An Appllcatron to M drkov Chdlns (O ptlonal) 96
Y .7za.'s'!ftïë C hapter 3 DETE RM I NA NTS 1 O 7
3.1 The Laplace Expanspon 107
3.Q Deterrnlnants dncl M dtrlx lnverses IQ0
3.3 An Applkcutlon to polyrlom la! knterpolatlon (O ptlonal) 1313.4 Proof of the Lupidce Expanslon (O ptlonal) 136
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:2* .4..tkWt?.u tt- hl i) p tkr i 4 bî L C 1 Q) R G E C) tb?b ET R Y ' z; :'7e '. Vectors arld Llnes 1 41/ 7 The Dot prorjuct dnd projectlons 1564.3 F'lanes and the Cross product 165
:1 + An Appllcatlon to Ledst Squares Approxlmatlon (O ptlorlal) 178
tztW ezz.tkW..4 C t kcl r) t e r 5 V E Q FO R h; PAC E$ ! .fJ ;'
5 2 Exam ples and 8asrc propertles 187
5.2 Subspaces and Spannrn: Sets 1985.-) Llnear kndepenclence and Dlm cnslon Q08
5..1 Exlstcnce of 8ases Q19-5.:L yank of a M atrlx QQ6.$.t:. An Appllcatlon to polynorzllals (O ptlonal) Q385. ? An Appllcdtlon to Dlfferential Equatlons (O ptlonal) Q44
:ju* mq.tkWK C hi'gp te ! t4 E iG E N VA LU ES A h1 D 1) IA G O INIA L I J..A7. l C'J i'x 'z ;' 5
tz. 1 Elgenvalues anci Slm lldrlAz Q516. :2 Dlagona I rzatlon Q616 .p O rthogonalzty In R '' Q7Qtii.lt O rthogondl Dlagonalizatlon Q81
b 'p posltlve Deflnlte M atrrces Q89
t$v6 Lp-Factorlzdtlon (O ptzonal) Q956. ' Cornputlng Eqkége:nvalues (O ptlorlar) Q#8/1J tl Com plk!x M atrlces (Q ptponal) 302f. 9 An Apphlcatlon to Q uadratlc Form s ûo ptlorldi) 313
(a. 'k t) A n A pplrcatlon to iest A pproxpm atlon arld Least Squares
(O ptlondl) 3Q4$.1 7 A n Appglcatlon to System s of Dlfferentlal Equatkons
(O ptlonal) 331
:J* .4.%W..4 C ha ptef 7 1-4 hl EA R Trt/kH S FO RM A TI O N S .'î )) ,7
7.1 Exarnples dnd Elem entaly Propertles 339'
.? .2 Kernel and Im age of a Llnear Transform atlon 35Q7 .
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o Isom orphlsrns dnd Com posrtlorl 3ô2
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7. fl The M dtrlx of a Llnedr Trunsform utlon 3717.5 Change of Basls 379
'J tl Invdrlant Subspaces and Dlrect Tum s 388'
.?. 7 Block TrlunbjuLdr Form 4.QQ
7 .8. An Appllcatkon to Llngar qecurrence keldtlons (O ptlondl) 41 ()
* .4.x*114 (: hapter 8 I N >) E. 8.t PRO D U CT S IS#hC F '-:: zt :1 'i
8. 1 Inner proclucts untj Norm s 4Q1k'3.'2 O rlhorgonaf Sets of k'ectors 4311$.7 Clrthogonal Dlagonallzation 44.18.4 Isornetrles 448
8.5 g'A.s A ppllcatlon to Fourler A pproxlm atkon 460
't* i4.+ A p p e n cl I x ,,:v. C (3 A,$ P L E X S U M ï$' 8. R % . . (
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kr+lz.!s''l Appendix B f i.qi 7 iè':-.1 3 9 ; u'- 'r k ('J N 'rt.7 : b >.: i! .q !''t s7 i.-tht', f'r bf ..'.>''.p.!. '' . t ' ... .('.'
tlJ. : Grdphlcal M ethods 4.81$$.Q' Tine Skrqlple:x A lgorlthm 489
zr g'z?x A p pend ix C rvS..?.k ! @' ) @'.' M A T k QA t ! 8 1) b ('. ?. O 2%1 . '
L'+ 2+ SELECTED A NSW ERS 507
ztp iz?g I N DEX 531
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