Fundamentals of Matrix Algebra, 2011a

More documents

Recommendations

Info

Contents Thanks Preface Table of Contents iii v vii 1 Systems of Linear Equaons 1 1.1 Introducon to Linear Equaons . . . . . . . . . . . . . . . . . . . . 1 1.2 Using Matrices To Solve Systems of Linear Equaons . . . . . . . . . 5 1.3 Elementary Row Operaons and Gaussian Eliminaon . . . . . . . . . 12 1.4 Existence and Uniqueness of Soluons . . . . . . . . . . . . . . . . . 22 1.5 Applicaons of Linear Systems . . . . . . . . . . . . . . . . . . . . . 34 2 Matrix Arithmec 45 2.1 Matrix Addion and Scalar Mulplicaon . . . . . . . . . . . . . . . 45 2.2 Matrix Mulplicaon . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.3 Visualizing Matrix Arithmec in 2D . . . . . . . . . . . . . . . . . . . 66 2.4 Vector Soluons to Linear Systems . . . . . . . . . . . . . . . . . . . 80 2.5 Solving Matrix Equaons AX = B . . . . . . . . . . . . . . . . . . . . 97 2.6 The Matrix Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 2.7 Properes of the Matrix Inverse . . . . . . . . . . . . . . . . . . . . 112 3 Operaons on Matrices 121 3.1 The Matrix Transpose . . . . . . . . . . . . . . . . . . . . . . . . . . 121 3.2 The Matrix Trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 3.3 The Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 3.4 Properes of the Determinant . . . . . . . . . . . . . . . . . . . . . 146 3.5 Cramer’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 4 Eigenvalues and Eigenvectors 163 4.1 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . . . 163 4.2 Properes of Eigenvalues and Eigenvectors . . . . . . . . . . . . . . 177
Page 1: . . . Fundamentals of Matrix Algebr
Page 4 and 5: Copyright © 2011 Gregory Hartman L
Page 7: P A Note to Students, Teachers, and
Page 11 and 12: 1 . S L E You have probably encoun
Page 13 and 14: 1.1 Introducon to Linear Equaons 1.
Page 15 and 16: 1.2 Using Matrices To Solve Systems
Page 23 and 24: 1.3 Elementary Row Operaons and Gau
Page 29 and 30: 2R 2 + R 3 → R 3 1.3 Elementary R
Page 33 and 34: 1.4 Existence and Uniqueness of Sol
Page 45 and 46: 1.5 Applicaons of Linear Systems eq
Page 47 and 48: 1.5 Applicaons of Linear Systems (N
Page 49 and 50: 1.5 Applicaons of Linear Systems We
Page 51 and 52: 1.5 Applicaons of Linear Systems Re
Page 53 and 54: 1.5 Applicaons of Linear Systems (G
Page 55 and 56: 2 . M A A B B ′ A ′ A fundament
Page 57 and 58: 2.1 Matrix Addion and Scalar Mulpli
Page 59 and 60:
2.1 Matrix Addion and Scalar Mulpli
Page 61 and 62:
2.2 Matrix Mulplicaon 9. −2A −
Page 63 and 64:
2.2 Matrix Mulplicaon We have been
Page 65 and 66:
2.2 Matrix Mulplicaon Two quick not
Page 67 and 68:
2.2 Matrix Mulplicaon m 32 = [ −2
Page 69 and 70:
2.2 Matrix Mulplicaon S We will fin
Page 71 and 72:
2.2 Matrix Mulplicaon 3. [ ] ([ ] [
Page 73 and 74:
2.2 Matrix Mulplicaon in detail onc
Page 75 and 76:
2.2 Matrix Mulplicaon ⎡ −1 0
Page 77 and 78:
2.3 Visualizing Matrix Arithmec in
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Before compung the length of || −
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
2.4 Vector Soluons to Linear System
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
2.5 Solving Matrix Equaons AX = B [
Page 109 and 110:
2.5 Solving Matrix Equaons AX = B W
Page 111 and 112:
2.5 Solving Matrix Equaons AX = B W
Page 113 and 114:
2.6 The Matrix Inverse These queson
Page 115 and 116:
2.6 The Matrix Inverse Let’s chec
Page 117 and 118:
2.6 The Matrix Inverse gives us [ 1
Page 119 and 120:
2.6 The Matrix Inverse S Since ad
Page 121 and 122:
2.6 The Matrix Inverse Knowing a ma
Page 123 and 124:
2.7 Properes of the Matrix Inverse
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
3 . O M In the previous chapter we
Page 133 and 134:
3.1 The Matrix Transpose . Ḋefini
Page 135 and 136:
3.1 The Matrix Transpose Find (AB)
Page 137 and 138:
3.1 The Matrix Transpose kA T . Thi
Page 139 and 140:
3.1 The Matrix Transpose symmetric.
Page 141 and 142:
3.2 The Matrix Trace 21. 22. ⎡ 1
Page 143 and 144:
3.2 The Matrix Trace It isn’t exa
Page 145 and 146:
3.3 The Determinant Exercises 3.2 I
Page 147 and 148:
3.3 The Determinant . Example 68 Fi
Page 149 and 150:
B 4,3 = ∣ 1 2 8 −3 5 2 −1 9 6
Page 151 and 152:
3.3 The Determinant This secon is e
Page 153 and 154:
3.3 The Determinant so let’s get
Page 155 and 156:
3.3 The Determinant In the next sec
Page 157 and 158:
3.4 Properes of the Determinant We
Page 159 and 160:
3.4 Properes of the Determinant kno
Page 161 and 162:
3.4 Properes of the Determinant Let
Page 163 and 164:
3.4 Properes of the Determinant and
Page 165 and 166:
3.4 Properes of the Determinant .
Page 167 and 168:
3.4 Properes of the Determinant ⎡
Page 169 and 170:
3.5 Cramer’s Rule 3.5 Cramer’s
Page 171 and 172:
3.5 Cramer’s Rule S Therefore The
Page 173 and 174:
4 . E E We have oen explored new i
Page 175 and 176:
4.1 Eigenvalues and Eigenvectors No
Page 177 and 178:
4.1 Eigenvalues and Eigenvectors .
Page 179 and 180:
4.1 Eigenvalues and Eigenvectors sh
Page 181 and 182:
4.1 Eigenvalues and Eigenvectors We
Page 183 and 184:
4.1 Eigenvalues and Eigenvectors
Page 185 and 186:
4.1 Eigenvalues and Eigenvectors Fo
Page 187 and 188:
4.2 Properes of Eigenvalues and Eig
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195:
Page 198 and 199:
Chapter 5 Graphical Exploraons of V
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
Chapter A Soluons To Selected Probl
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248:
Index parcular soluon, 30 problem s
show all

Fundamentals of Matrix Algebra, 2011a

Create successful ePaper yourself

Delete template?

Save as template?