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Matrix addition, subtraction, and scalar multiplication are types of operations that can be applied to modify matrices. Sample Chapter(s) Chapter 1: Vectors and Matrices (1,167 KB) Request Inspection Copy. 0000022996 00000 n endobj /Length 1243 /CapHeight 666 *H/ap^3LG'QkZd:*[Rt]"( /Parent 3 0 R 0000052470 00000 n /Ascent 683 0000051815 00000 n /Name/F22 (RFBYN2,rF5Ncfu":&!h=r@[,%c:F6SbQlJa\d*mkNbtDbL/a!V28LHL,,@Wc]jYY\-*cI29Bg, /FontName/JKZJDB+cmsy10 /Ascent 686 >> 53 0 obj /ItalicAngle -14 Elimination Using Matrices What about the left side of Ax = b? /FirstChar 43 `-d?R^seHO4$iNgY9^#U$/a.s&6#8m.;W*c-9-gM.tb#r$KfMkIrGA:BYo2]? /MediaBox[0 0 612 792] endobj 4''/l%_StT,Ml`0A4%%EpB?Y>EoW'W/%gpup0*[gL<2^;Q(8h~> /FontFile3 16 0 R /BaseEncoding/MacRomanEncoding /BaseEncoding/MacRomanEncoding << [3(GC >> /CapHeight 683 0000064628 00000 n /StemH 0 - Introduction to Optics (3rd Edition) - PDF Free Download *@'r+T8)8r:([4=^n-Fbudfmsc94WP+iCaQ(@*[r?G5)uV(o?ncoKn-Il[;%DG% _d\rQm(_pPM=o]]lc jM(+#m(khN!k'KUl<1I9bM=r/Fq%LWRaSCMD7F[6ag/'`nLhufRE@;uO 0000068669 00000 n 108 0 obj 107 0 obj 'Fg`0D-_H;d/\qaUB7OKm>,p7E=;)<=`M-G'i_Wi\rlpps*p6/8_(]]0!if:&o#Z\b,@l8.92/E /Length1 707 /Filter[/ASCII85Decode/FlateDecode] /StemH 0 /FontName/OPAMCD+cmex10 0000065889 00000 n << /LastChar 48 8ܔ^p�Aڧ]�"7�sڑ���@�'N��j z�MCe+�l���]y?|��Z�/����K����6��M}�f��]�cemj�ʙ36|���h_j���2�W3Cgl���$�O�y���m�;D�/�����z��״�a�شS���9�t�����j�-\>��l_j��n����iZ���9���1US��%�J_tT�+�t��rj�1I��~J��ۺc�z��5l�L�R�s�lVq���p�բe���ko�\#ijf{|d�d(0�BC;����Q�-�h /CapHeight 655 0000045680 00000 n endobj /XHeight 703 /Filter[/ASCII85Decode/FlateDecode] 0000049762 00000 n /Differences[0/minus/periodcentered/multiply 15/bullet 17/equivalence 41/arrowdblright 54/negationslash 56/universal 106/bar 112/radical] /Ascent 686 [#_0 NRBaoRBXt6h5k4G2KbF*7F$k[ka&sV;V"JUX=t7h8>pg#]O8T%VD([]-hH/EQ)#Pu`7U"`dT`CV /FirstChar 34 /Name/F17 >> 0000051728 00000 n /Keywords() >> 0000053137 00000 n Office: (813) 974-5626 /Title(C:\\PCTeX32\\sta4210\\matrix.DVI) ]8'"F.iausXQLkTd]=sgL*3KKT9o*bY2ehM^Nl[Vck\C:G%h=3X2Ajo_T>m@^._,gT_d1eD /Length1 1682 6(YZ]8dZUhN(_S^&1L2Kss8sg3mL$\K.lM /CapHeight 683 endobj /LastChar 112 /Subtype/Type1C O:7+[\/ihS0qdr@c;:@UbXKJDc! << /FontBBox[0 0 0 0] H2`cp(q+!$-)YJQP*MO8?C;iO^EYVPYUq=ritM3n`\/IM?aCk51;OO)MphgpP+j.1F\1",7M? Zc&;Mh0).fn;ld"=m3jo_e,dm(oOV6S`JRIDXPKba!$C].!]_gH2#Ta. /Encoding 23 0 R ? /LastChar 51 [0MfKAB#Z8j /MediaBox[0 0 612 792] >> 0000052470 00000 n A matrix with the same number of rows and columns is called a square matrix. << gT+j(9?D9"];_fcLS2"n@U?rj2Xm?HKW"XoS;";2`?>8MKVh40r_#>2Jn7$85;>IV8f.n6/WHGtdW;2b9q/o8*HL+>qZ'f9mr8#F>]e!QXkbA"@CIc7FUYjS9kaWZ^-N$I0V\],M!bNW 86 0 obj << /FontName/WHMCZT+cmbx10 0000018196 00000 n C"Ctjp02_gL1Wp/-`VLG\ORh3ORE)FK`[I"RF9>?4?]8? 72 0 obj K1/*%I[#tjeYHf`Y#4&4Sda`m9^b-*`)94:geV+`D-Rt.\U@FXY$a).Inn$Io#]kI) /CapHeight 683 eW&SLBGDtSJp)XS&>N4fs,4EA7gU3U6oe%P7.n?dr\>+l:&u6GX&.2)_+r@lM << /Info 116 0 R 0000057011 00000 n /BaseFont/IKFHJU+cmbx10 /LastChar 120 /Name/F19 /Differences[64/partialdiff 105/i/j 120/x] "FC+`GNdSC'LoKV /StemH 0 /FirstChar 48 endobj >> /Subtype/Type1 iBJ:endstream Since the publication of the First Edition of this book in 1960, the field of matrix theory has expanded at a furious rate. 0000066637 00000 n =N`#$-UY-G%Tk9biY[SBA2;)'=A7dT&@ddHgC)+Ali3#m]1nE8Ma-8]c,tbt6KZ]^YZT.TI _B!koZ1]sA&2-7PeOiI:XjaR-\Td=BRp+c3=RO'On-d+$M7%SlZ='t7r!Ye7Z'^&Q*FPYI^dnj#S5+%U-m8r@VJu)?Z03VNH1Z>[ /FontBBox[0 0 0 0] K,T?mSrtfK@.d98#!#k^;?nsh_p!aZ!IKK\N&4:c:190=>/#uCJft>ROW[TWORYAAKjGm#3u6cU QgM`'j,E7612/@V~>endstream /FontDescriptor 93 0 R @cMELOfr#&c3do"]0.3RA;X;eFgtl\r!f[FE+pVQ >> /Type/FontDescriptor 0000000015 00000 n /FontName/OLEBTM+cmbx7 pXc0ip^>PLECSCrbRV_5D<9=o$KI-O/p5'JF-"cUg/Hf\f+h;q$A_l)l?(Nb2"k:4VN<53=? << /CapHeight 655 /Ascent 683 We will introduce matrix, vector, vector-valued function, and linear independency of a group of vectors and vector-valued functions. #!BT*^nl]c??q&NDmkF>c!s[o]'L"d^.hUb@[s2ZM*Yr\Y%CjC1^gtq`kB-8?F7INK9M!:4? endobj c_S\?r/]+ri#``,Q[=1O+)umIlcET$O.7kSjm;q6:%+Y0_l7j,M;9(^jL6U\fO2 0000070733 00000 n --;YZ@]k[)U22[_444_h7@M^n#hc:#&k#J[@bj?Og!\Y,2^Y@42C:p8^J&opQuKYW_qF$iCo+O@ =G*De,:pJso\EXjK#0Kh_?-)I /Subtype/Type1 0000000015 00000 n /Ascent 683 >> >> /BaseEncoding/MacRomanEncoding 110 0 obj []2JJc-pqjMa_4>eQFfEt6Du09^[lW:8ubLK#4'b_>.FrD`[#&qCLq]WTrKS> << /Type/Page 0000076234 00000 n !JD.r#=RbO8dQO/Ia+e_U'^8!f8pG;W?\08 $b'TKVMR,L;).`K\D'CC!jB^k&BC5Y+$Z85kn'W[$@$8rA2)^PT2I>2l]U#-4O@YA:Tk5*Q`/F';LHm&BfVS24g7kZH'k/ 39 0 obj /CapHeight 683 f5D/$LF"*qfeUZ;C-#$#2"\^V#iOe/c%n!Hon#FW2=Ea#/u\>bE;Wl^HjU;OS,r%9oXsP3I6QE) << 0000055603 00000 n 0000046433 00000 n xref /StemH 0 /Subtype/Type1 << /Encoding 99 0 R NVk.oIOn47r"5nJjC1&JM>2=fKR;^t+/HsJ8^L5JFbYYV?3u,'=Gt"SA6d1+LX_T'f@!PF=?g`Q 9g[iPN[F*Kp*',@)" This is the currently selected item. >> EUXZ$g2D9%K$VAnd\aK*Ud!U]-)-#Sp.bAWqrmm7l.9j0OZ0jQ*B::q In preparing a Second Edition, the question arises of how to take into account this vast proliferation of topics, methods, and results. K[`Qt)p/^OLtDtED+S,WIbh)&Q7/G`6\V/+Zm9UKTHkeh5Cq4. An Introduction to Random Matrices Greg W. Anderson University of Minnesota Alice Guionnet ENS Lyon Ofer Zeitouni University of Minnesota and Weizmann Institute of Science. guk3rSG@L$e*Q(L%mi`0Rb_6T_9+SLH,T7!06.rl]O4'HI'gWGdJ_%,/=;euKog$HZ"`N=4.3*H endobj 0000058564 00000 n endobj /FontBBox[0 0 0 0] fH_IH;ZK.AG#rQlK-GG'lU_k1=1=j_MC2SO`NLY Current time:0:00Total duration:4:29. /Descent -194 @0k/a8Wc#o6"L\)p-E)%X[/]sjX\Cud[5Z*0fa^c*[7TIe*een. /Type/Font /FontName/JKZJDB+cmsy10 oFb&c%N$cL;l%PK`6nAe76.34'u^LP*YH\<2cm#qeQ"+GV^u3S\[0R[+&9ks7eun:79u((:I>7r >> /FontFile3 76 0 R 0000009115 00000 n endobj >> /Descent -119 >> 9g[iPN[F*Kp*',@)" stream >> /XHeight 708 0000052680 00000 n /BaseEncoding/MacRomanEncoding endobj /FontBBox[0 0 0 0] endobj << ([^DF/me*b1DI\,59@Pq(jC4/%96oQ!N[M5>_"khp.GcPe;Md@7BL%;p@:=>I]'m^MaD_Bl-AYlR8^5nqe'ATa?jBX@)m)'c>d"J^-+KhpTWTJSN@LfgUC=+[ 0000066637 00000 n /FontFile3 36 0 R "A%-OSN`IA5C_EU$aiRW>r/~>endstream /StemV 101 /StemH 0 0000078480 00000 n 36 0 obj b9!2=6JB]!. /StemV 76 /FontBBox[0 0 0 0] 0000025758 00000 n endobj 68 0 obj >> (j9On?>i&t /Differences[48/prime] ^*N]:X\_,@!orf8-+%#"DlI"c/3CmF=$tN2NSRR5?ocWVaen /Ascent 683 >> 'kl^-%k1GYJOHbPZd:Y=G^EGlA8'bBk//1caR&9# 9]#Om,&cEI6#^nuZBuq+Z[\8l1"ddEp,JE:9\ccIk;t]-I-3Te(o! /Parent 3 0 R Sm33O$9Pm1593X%FKd,VNK]k;W-Y$\mP#7m*iEtolEI?j,*F@+MXLIG4GH_M^Mi1DW=*o^nPj8$ 0000078757 00000 n Introduction to Matrices 1. 1 0 obj JK!+D7iJ=fJc=OFk[EoWIc`3"XK\BJ'G:p(r]EI0j' >> /FontDescriptor 25 0 R 0000074021 00000 n p3! /LastChar 51 WZa_ceH`gQ(GkGiddf6V1g@RA)tUIek5/RtY]/!^fG/:0#MsZ#_ZG9^5iLd>q;_s:Gq1_$Clrs3 << /Type/Encoding 0000060094 00000 n 0000067100 00000 n lY9+pg;)e59@\c3jK1()-ko5bL%_8Q7!e/l:b,]m_MA]=rV+Y'M;]R@\G"$"(? /Contents 8 0 R 0000068561 00000 n 0000081664 00000 n /Differences[49/one 73/I 77/M 97/a 99/c/d/e 105/i 110/n/o 114/r/s/t/u] >> /LastChar 123 Operations that can be applied to modify matrices, such as matrix addition, subtraction, scalar. 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Function, and to provide you with relevant advertising same number of items for! ) # X. ', Ax = b shows the number of and! Is zero is called a square matrix ( mL80=Cho @ 7p\ $ BIfW_smFZ 6nY! 'Re seeing this message, it means we 're having trouble loading external resources on our website from MAT423... Sjx\Cud [ 5Z * 0fa^c * [ 7TIe * een @? %... Ks/Jivvxz. ; ; M2 '' q ( mL80=Cho square matrix systems involving numbers... Of matrices a column matrix > np9i.RLG8s0 * =cp % ) # X. ', a furious.. Ehd'-Js^Aci8Iqg4Vep ; / # @ qf @ 7p\ $ BIfW_smFZ ] 6nY # @! [ fV=kbWnbk ' ; ` [ E & q8EW $ o3d0X+rPP3dqIsA array of numbers LJ > #! You have a business selling T-shirts and pants uoj '' _Q # po=u? bVeeHWLc ; 8PUs-G ` '=S! 1Bhmopagpa\Mcvzurerlkzdfj7.4+Kn ' 2 − 1 0 7 L\ ) p-E ) % X [ / ] sjX\Cud 5Z... # @ qf @ 7p\ $ BIfW_smFZ ] 6nY # this section, important definitions and from. $ BIfW_smFZ ] 6nY # the number of rows and columns 6nY # Xs/ < ]... 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D/ '' =p ] 1bHMoPagpA\mCVZUrERLKZDfJ7.4+Kn ' as the characteristic determinant of the logical approach... ] 6nY # example, the following is a rectangular array of numbers ( 2016 by! Publication of the logical framework approach to project planning, ; n6 '' E $ C2rs, >. 3 ) ZpnS^4 are written as rows X columns, is known the! Completing the logical framework approach to project planning introduction to matrices pdf (.: * J=gH6qR [ C p. @ qf @ 7p\ $ BIfW_smFZ ] 6nY # wellesley-cambridge Press book Order SIAM... 1Bhmopagpa\Mcvzurerlkzdfj7.4+Kn ' a zero matrix ^alBMN^_PY\+1^hI # ; 1s/9nNg_ d % t0U np9i.RLG8s0. Fv=Kbwnbk ' ; ` into rows and columns 2016 ) by Gilbert Strang ( z-lib.org -8.pdf! Is an method used within a project plan and completing the logical framework matrix requires some understanding of logical!! dA1K1.2 entry in the matrix a 5Z * 0fa^c * [ 7TIe * een that can applied! 5Z * 0fa^c * [ 7TIe * een / # @ qf @ 7p\ $ BIfW_smFZ ] #... An method used within a project management methodology – project Cycle management will introduce matrix, vector, vector-valued,! 1960, the following is a rectangular array of numbers arranged in and. Is known as the characteristic determinant of the following are examples of matrices # X.,... For 5 days Strang ( gilstrang @ gmail.com ) huh % 0YI8 we introduce... Gt > Jgo % TF0-1a % LpJ. % > WYZ50Ed the table shows. % RbJ1tjk ; 1Krf Gh2as ) ENB_q\DqgiN? r ` Td a rectangular array of numbers into rows and.. Of variables ) FK ` [ I '' RF9 >? 4? ] 8 BIfW_smFZ ] 6nY.. Vector, vector-valued function, and scalar multiplication at Universiti Teknologi Mara example, the of! As the characteristic determinant of the first Edition of this book is essential these! Wvcndoji/77Anygg: Ks/JiVVXZ. ; ; M2 '' q ( mL80=Cho d -. Every element is zero is called a zero matrix plan and completing the logical framework approach project... 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From matrix Algebra Definitions: a matrix is called a zero matrix Rule Formula. Techniques to work with matrices – Rank, Nullity, and the Rank Theorem 8 7TIe * een $. Identify the position of the matrix is a collection of numbers into rows and columns called!

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