线性代数（英文版·第9版）

Contents
Preface ix
1 Matrices and Systems of Equations 1
1.1Systems of Linear Equations 1
1.2 RowEchelonForm11
1.3Matrix Arithmetic 27
1.4Matrix Algebra 46
1.5Elementary Matrices 60
1.6Partitioned Matrices 70
MATLABExercises80
ChapterTestA—TrueorFalse84
Chapter Test B 85
2 Determinants87
2.1The Determinant of a Matrix 87
2.2Properties of Determinants 94
2.3Additional Topics and Applications 101
MATLABExercises109
ChapterTestA—TrueorFalse111
Chapter Test B 111
3 Vector Spaces112
3.1 Definition and Examples 112
3.2 Subspaces 119
3.3 Linear Independence 130
3.4 Basis and Dimension 141
3.5 Change of Basis 147
3.6 Row Space and Column Space 157
MATLABExercises165
ChapterTestA—TrueorFalse166
Chapter Test B 167
4 Linear Transformations169
4.1De.nition and Examples 169
4.2Matrix Representations of Linear Transformations 178
4.3Similarity 192
MATLABExercises198
ChapterTestA—TrueorFalse199
Chapter Test B 200
5 Orthogonality201
5.1The Scalar Product in Rn 202
5.2Orthogonal Subspaces 217
5.3Least Squares Problems 225
5.4Inner Product Spaces 238
5.5Orthonormal Sets 247
5.6The Gram–Schmidt Orthogonalization Process 266
5.7Orthogonal Polynomials 275
MATLABExercises283
ChapterTestA—TrueorFalse285
Chapter Test B 285
6 Eigenvalues287
6.1Eigenvaluesand Eigenvectors288
6.2Systems of Linear Differential Equations 301
6.3Diagonalization 312
6.4Hermitian Matrices 330
6.5The Singular Value Decomposition 342
6.6Quadratic Forms 356
6.7Positive De.nite Matrices 370
6.8Nonnegative Matrices 377
MATLABExercises387
ChapterTestA—TrueorFalse393
Chapter Test B 393
7 Numerical Linear Algebra395
7.1Floating-Point Numbers 396
7.2Gaussian Elimination 404
7.3PivotingStrategies409
7.4Matrix Norms and Condition Numbers 415
7.5Orthogonal Transformations 429
7.6The Eigenvalue Problem 440
7.7Least Squares Problems 451
MATLABExercises463
ChapterTestA—TrueorFalse468
Chapter Test B 468
8 Iterative MethodsOnline.
8.1Basic Iterative Methods
9 Canonical FormsOnline.
9.1Nilpotent Operators
9.2The Jordan Canonical Form
Appendix:MATLAB471
Bibliography 483
Answers to Selected Exercises 486
Index 499
. Online: The supplemental Chapters 8 and 9 can be downloaded from the Internet. See the section of the Preface on supplementary materials.

前言
第1章　矩阵与方程组1
1.1　线性方程组1
1.2　行阶梯形11
1.3　矩阵算术27
1.4　矩阵代数46
1.5　初等矩阵60
1.6　分块矩阵70
练习80
第2章　行列式87
2.1　矩阵的行列式87
2.2　行列式的性质94
2.3　附加主题和应用101
练习109
第3章　向量空间112
3.1　定义和例子112
3.2　子空间119
3.3　线性无关130
3.4　基和维数141
3.5　基变换147
3.6　行空间和列空间157
练习165
第4章　线性变换169
4.1　定义和例子169
4.2　线性变换的矩阵表示178
4.3　相似性192
练习198
第5章　正交性201
5.1　Rn中的标量积202
5.2　正交子空间217
5.3　最小二乘问题225
5.4　内积空间238
5.5　正交集247
5.6　格拉姆–施密特正交化过程266
5.7　正交多项式275
练习283
第6章　特征值287
6.1　特征值和特征向量288
6.2　线性微分方程组301
6.3　对角化312
6.4　埃尔米特矩阵330
6.5　奇异值分解342
6.6　二次型356
6.7　正定矩阵370
6.8　非负矩阵377
练习387
第7章　数值线性代数395
7.1　浮点数396
7.2　高斯消元法404
7.3　主元选择策略409
7.4　矩阵范数和条件数415
7.5　正交变换429
7.6　特征值问题440
7.7　最小二乘问题451
练习463
附录　MATLAB471
参考文献483
部分练习参考答案486