简介
线性代数是处理矩阵和向量空间的数学分支科学，在现代数学的各个领域都有应用。《线性代数及其应用(第3版)(英文版)》主要包括线性方程组、矩阵代数、行列式、向量空间、特征值和特征向量、正交性和最小二乘方、对称矩阵和二次型等内容。《线性代数及其应用(第3版)(英文版)》的目的是使学生掌握线性代数最基本的概念、理论和证明。首先以常见的方式，具体介绍了线性独立、子空间、向量空间和线性变换等概念，然后逐渐展开，最后在抽象地讨论概念时，它们就变得容易理解多了。这是一本介绍性的线性代数教材，内容翔实，层次清晰，适合作为高等院校理工科数学课的双语教学用书，也可作为公司职员及工程学研究人员的参考书。
目录
chapter 1 linear equations in linear algebra 1
introductory example: linear models in economics and engineering 1
1.1 systems of linear equations 2
1.2 row reduction and echelon forms 14
1.3 vector equations 28
1.4 the matrix equation ax = b 40
1.5 solution sets of linear systems 50
1.6 applications of linear systems 57
1.7 linear independence 65
1.8 introduction to linear transformations 73
1.9 the matrix of a linear transformation 82
1.10 linear models in business, science, and engineering 92
supplementary exercises 102
chapter 2 matrix algebra 105
introductory example: computer models in aircraft design 105
2.1 matrix operations 107
2.2 the inverse of a matrix 118
2.3 characterizations of invertible matrices 128
2.4 partitioned matrices 134
2.5 matrix factorizations 142
.2.6 the leontief input-output model 152
2.7 applications to computer graphics 158
2.8 subspaces of rn 167
2.9 dimension and rank 176
supplementary exercises 183
chpater 3 determinants 185
introductory example: determinants in analytic geometry 185
3.1 introduction to determinants 186
3.2 properties of determinants 192
3.3 cramer's rule, volume, and linear transformations 201
supplementary exercises 211
chpater 4 vector spaces 215
introductor.v example: space flight and control systems 215
4.1 vector spaces' and subspaces 216
4.2 null spaces, column spaces, and linear transformations 226
4.3 linearly independent sets; bases 237
4.4 coordinate systems 246
4.5 the dimension of a vector space 256
4.6 rank 262
4.7 change of basis 271
4.8 applications to difference equations 277
4.9 applications to markov chains 288
supplementary exercises 299
chpater 5 eigenvalues and eigenvectors 301
introductory example: dynamical systems and spotted owls 301
5.1 eigenvectors and eigenvalues 302
5.2 the characteristic equation 310
5.3 diagonalization 319
5.4 eigenvectors and linear transformations 327
5.5 complex eigenvalues 335
5.6 discrete dynamical systems 342
5.7 applications to differential equations 353
5.8 iterative estimates for eigenvalues 363
supplementary exercises 370
chpater 6 orthogonality and least squares 373
introductory example: readjusting the north american datum 373
6.1 inner product, length, and orthogonality 375
6.2 orthogonal sets 384
6.3 orthogonal projections 394
6.4 the gram-schmidt process 402
6.5 least-squares problems 409
6.6 applications to linear models 419
6.7 inner product spaces 427
6.8 applications of inner product spaces 436
supplementary exercises 444
chpater 7 symmetric matrices and quadratic forms 447
introductory example: multichannel image processing
7.1 diagonalization of symmetric matrices 449
7.2 quadratic forms 455
7.3 constrained optimization 463
7.4 the singular value decomposition 471
7.5 applications to image processing and statistics 482
supplementary exercises 491
appendixes
a uniqueness of the reduced echelon form a1
b complex numbers a3
glossary a9
answers to odd-numbered exercises a19
index i1
introductory example: linear models in economics and engineering 1
1.1 systems of linear equations 2
1.2 row reduction and echelon forms 14
1.3 vector equations 28
1.4 the matrix equation ax = b 40
1.5 solution sets of linear systems 50
1.6 applications of linear systems 57
1.7 linear independence 65
1.8 introduction to linear transformations 73
1.9 the matrix of a linear transformation 82
1.10 linear models in business, science, and engineering 92
supplementary exercises 102
chapter 2 matrix algebra 105
introductory example: computer models in aircraft design 105
2.1 matrix operations 107
2.2 the inverse of a matrix 118
2.3 characterizations of invertible matrices 128
2.4 partitioned matrices 134
2.5 matrix factorizations 142
.2.6 the leontief input-output model 152
2.7 applications to computer graphics 158
2.8 subspaces of rn 167
2.9 dimension and rank 176
supplementary exercises 183
chpater 3 determinants 185
introductory example: determinants in analytic geometry 185
3.1 introduction to determinants 186
3.2 properties of determinants 192
3.3 cramer's rule, volume, and linear transformations 201
supplementary exercises 211
chpater 4 vector spaces 215
introductor.v example: space flight and control systems 215
4.1 vector spaces' and subspaces 216
4.2 null spaces, column spaces, and linear transformations 226
4.3 linearly independent sets; bases 237
4.4 coordinate systems 246
4.5 the dimension of a vector space 256
4.6 rank 262
4.7 change of basis 271
4.8 applications to difference equations 277
4.9 applications to markov chains 288
supplementary exercises 299
chpater 5 eigenvalues and eigenvectors 301
introductory example: dynamical systems and spotted owls 301
5.1 eigenvectors and eigenvalues 302
5.2 the characteristic equation 310
5.3 diagonalization 319
5.4 eigenvectors and linear transformations 327
5.5 complex eigenvalues 335
5.6 discrete dynamical systems 342
5.7 applications to differential equations 353
5.8 iterative estimates for eigenvalues 363
supplementary exercises 370
chpater 6 orthogonality and least squares 373
introductory example: readjusting the north american datum 373
6.1 inner product, length, and orthogonality 375
6.2 orthogonal sets 384
6.3 orthogonal projections 394
6.4 the gram-schmidt process 402
6.5 least-squares problems 409
6.6 applications to linear models 419
6.7 inner product spaces 427
6.8 applications of inner product spaces 436
supplementary exercises 444
chpater 7 symmetric matrices and quadratic forms 447
introductory example: multichannel image processing
7.1 diagonalization of symmetric matrices 449
7.2 quadratic forms 455
7.3 constrained optimization 463
7.4 the singular value decomposition 471
7.5 applications to image processing and statistics 482
supplementary exercises 491
appendixes
a uniqueness of the reduced echelon form a1
b complex numbers a3
glossary a9
answers to odd-numbered exercises a19
index i1
Linear algebra and its applications
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