作者GILBERT STRANG为Massachusetts Institute of Technology数学系教授。从UCLA博士毕业后一直在MIT任教.教授的课程有“数据分析的矩阵方法”“线性代数”“计算机科学与工程”等，出版的图书有Linear Algebra and Learning from Data (NEW)、See math.mit.edu/learningfromdata、Introduction to Linear Algebra - Fifth Edition 、Contact linearalgebrabook@gmail.com、Complete List of Books and Articles、Differential Equations and Linear Algebra。

Gilbert Strang的《线性代数（第5版）》是一本经典线性代数教材。此书深入浅出地展示了线性代数的所有核心概念，讲述过程中恰当穿插了各种应用，体现了线性代数极端有用的思想。

Table of Contents
1 Introduction to Vectors 1
1 1 VectorsandLinearCombinations                       2

1 2 LengthsandDotProducts                           11

1 3 Matrices                                     22

2 Solving Linear Equations 31
2 1 VectorsandLinearEquations                         31

2 2 TheIdeaofElimination                            46

2 3 EliminationUsingMatrices                          58

2 4 RulesforMatrixOperations                          70

2 5 InverseMatrices                                83

2 6 Elimination = Factorization: A = LU                    97

2 7 TransposesandPermutations                          108

3 Vector Spaces and Subspaces 122
3 1 SpacesofVectors                                122

3 2 The Nullspace of A: Solving Ax = 0and Rx =0             134

3 3 The Complete Solution to Ax = b                       149

3 4 Independence,BasisandDimension                      163

3 5 DimensionsoftheFourSubspaces                       180

4 Orthogonality 193
4 1 OrthogonalityoftheFourSubspaces                                         193
4 2 Projections                                   205

4 3 LeastSquaresApproximations                         218

4 4 OrthonormalBasesandGram-Schmidt                                      232
5 Determinants 246
5 1 ThePropertiesofDeterminants                        246

5 2 PermutationsandCofactors                          257

5 3 Cramer’sRule,Inverses,andVolumes                                       272
vii

6 Eigenvalues and Eigenvectors 287
6 1 IntroductiontoEigenvalues                          287

6 2 DiagonalizingaMatrix                             303

6 3 SystemsofDifferentialEquations                       318

6 4 SymmetricMatrices                              337

6 5 PositiveDe niteMatrices                           349

7 TheSingularValueDecomposition (SVD) 363
7 1 ImageProcessingbyLinearAlgebra                      363

7 2 BasesandMatricesintheSVD                         370

7 3 Principal Component Analysis (PCA by the SVD)                           381
7 4 TheGeometryoftheSVD                           391

8 LinearTransformations 400
8 1 TheIdeaofaLinearTransformation                      400

8 2 TheMatrixofaLinearTransformation                                      410
8 3 TheSearchforaGoodBasis                          420

9 ComplexVectorsand Matrices 429
9 1 ComplexNumbers                               430

9 2 HermitianandUnitaryMatrices                        437

9 3 TheFastFourierTransform                          444

10 Applications 451
10 1GraphsandNetworks                              451

10 2MatricesinEngineering                            461

10 3 Markov Matrices, Population, and Economics                               473
10 4LinearProgramming                              482

10 5 Fourier Series: Linear Algebra for Functions                                 489
10 6ComputerGraphics                               495

10 7LinearAlgebraforCryptography                       501

11 NumericalLinear Algebra 507
11 1GaussianEliminationinPractice                        507

11 2NormsandConditionNumbers                        517

11 3 IterativeMethodsandPreconditioners                                       523
12LinearAlgebrain Probability& Statistics 534
12 1Mean,Variance,andProbability                        534

12 2 Covariance Matrices and Joint Probabilities                                 545
12 3 Multivariate Gaussian and Weighted Least Squares                         554
MatrixFactorizations 562
Index 564
SixGreatTheorems/LinearAlgebrain aNutshell 573