/ItalicAngle 0 hfniNdD*[^s?FE]*ft(E^fo"A8_MA@B.&^:k/1TIq(5Scp`CY"T&W'GoR^]QJIdN"=i-+&1&T.g,'5e3+nkKE`8& >> /FontDescriptor 37 0 R 105 0 obj << >> 0000041468 00000 n /Flags 4 [WQ;1CDEN'>!eLd&RNiDGiSpnt /Descent -194 ;G%h[Yb5Zb^]82D?RRT^,dMS2 /FontBBox[0 0 0 0] o*?5r3<9=a87jLZKBCl\FhduYP2BU'VQnO9J>7k*cDTCqfX-I61J;PQ-.K&3KNO&Vd 33 0 obj 0000051815 00000 n TjRYNl^n.UhNL&04BSa1CZ:Pc@ila[P(2Y+JXg'TP6g4B%^L>j>W3\W*ipZ8@=_tr3PPd!@E]c!a? /FontDescriptor 113 0 R 0000065637 00000 n /Name/F9 /Type/Catalog *r7,&tJmFB. 0000080735 00000 n /ItalicAngle 0 /Descent -194 0000051123 00000 n << /Subtype/Type1C endobj /FontBBox[0 0 0 0] =G9ahI@n?22u. /Name/F21 /Resources<> -,39XX)0in'ijR^-#;2*--M>MEfcM")oPiLE-9tCNK1)X@8qC)nh!_-g+^tq\(;eJ]#/4s2! 43]uIHG/0Yjt9QVs#qRiK?nDPcpjO@)q&'d4dieiGI"VWW,'QOCf?DAXU@;)8qQ?YM. << /Type/Font 2 0 obj /ItalicAngle -14 /Encoding 79 0 R /Type/Font /Type/Font endobj (276n2/?I#i1:,OO1H.3,,Q]M\6="Ib'YE[;tKQS.YD]do9u7:gL/.`rWB /Parent 3 0 R 0000034830 00000 n endobj 0000082769 00000 n /Type/FontDescriptor '-6f,mG]$qr=7!Zg,KZC404&bHo3"\MFDJ08qXe?JH^P3gE4 The dimensions of a matrix are written as rows x columns. >> \#i%=E"P1!J=>#q /Name/F1 /Differences[64/partialdiff 105/i/j 120/x] 4'. 57 0 obj /ItalicAngle 0 xref Representing linear systems of equations with augmented matrices. >> Introduction to matrices To start off our introduction to matrices, we will first show you that a matrix is nothing but a convenient way to organize data with rows and columns. 3;hrFe']?Wh:eFrTc32`/TWKBCS"\q&>"8]k6([t(/[,#>A%poD? << J\LCmE!Pi>e3? 0+LTcL?Lg]<8k$^YM$@kTKBK]#0K76_\pd]bN>YA(J]1AaGRu6!K/4p/ZIp]+$VZaQ20.Fh/Tn` "V+n8!:TFiV4D!eEG[dXNd9t,fF%Cd)ct\n(pK>,'!e`UAn^Bi@Q-. << /Widths[568 568 568 0 0 0 0 0 0 0 0 0 878] /Subtype/Type1C endobj /Type/Encoding *0'S9>1,Y6^0IZrqa8e^m_a>Sc>Zff1.8!IDjg$=V"#7MCI/@^5qOD\7]D?j0B*WcgC[K:TX3Y?Db8cVhl:'!.VPB /MediaBox[0 0 612 792] endobj << 0000035553 00000 n 22%mZLWR'Pf:#%sI&XgN5'\R=9Mendstream >> << /BaseFont/HTEFBK+cmsy5 /CapHeight 683 /Size 117 << /Type/Encoding (C0`mKZC)0pH<=7n59$XLYW=! 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
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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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