線性代數(shù)（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　矩陣與方程組1
1.1　線性方程組1
1.2　行階梯形11
1.3　矩陣算術27
1.4　矩陣代數(shù)46
1.5　初等矩陣60
1.6　分塊矩陣70
練習80
第2章　行列式87
2.1　矩陣的行列式87
2.2　行列式的性質94
2.3　附加主題和應用101
練習109
第3章　向量空間112
3.1　定義和例子112
3.2　子空間119
3.3　線性無關130
3.4　基和維數(shù)141
3.5　基變換147
3.6　行空間和列空間157
練習165
第4章　線性變換169
4.1　定義和例子169
4.2　線性變換的矩陣表示178
4.3　相似性192
練習198
第5章　正交性201
5.1　Rn中的標量積202
5.2　正交子空間217
5.3　最小二乘問題225
5.4　內積空間238
5.5　正交集247
5.6　格拉姆–施密特正交化過程266
5.7　正交多項式275
練習283
第6章　特征值287
6.1　特征值和特征向量288
6.2　線性微分方程組301
6.3　對角化312
6.4　埃爾米特矩陣330
6.5　奇異值分解342
6.6　二次型356
6.7　正定矩陣370
6.8　非負矩陣377
練習387
第7章　數(shù)值線性代數(shù)395
7.1　浮點數(shù)396
7.2　高斯消元法404
7.3　主元選擇策略409
7.4　矩陣范數(shù)和條件數(shù)415
7.5　正交變換429
7.6　特征值問題440
7.7　最小二乘問題451
練習463
附錄　MATLAB471
參考文獻483
部分練習參考答案486