正版新书]线代数(第5版)(美)Gilbert Strang (吉尔伯特·斯特朗

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

. EliminationUsingMatrices......................... 58

2.4 RulesforMatrixOraios ........................ 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 OrthonormalBasesanGa-Schmidt. . . . . . . . . . . . . . . . . . . 2
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 TheSingularValueDecoition (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 . . . . . . . . . . . . . . . . . . . 5
12LinearAlgebrain Probability& Statistics 534
12.1Mean,Variance,andProbability ...................... 534

12.2 Covariance Matrices and Joint Probabilities . . . . . . . . . . . . . . . . 545
1. Multivariate Gaussian and Weighted Least Squares . . . . . . . . . . . . 554
MatrixFactorizations 562
Index 564
SixGreatTheorems/LinearAlgebrain aNutshell 573

作者GILBERT STRANG为Massachusetts Institute of Technology数学系教授。从UCLA博士后一直在MIT任教.教授的课程有“数据分析的矩阵方法”“线代数”“计算机科学与工程”等，出版的图书有Linear Algebra and Learning from Data (NEW)、See mat.i.eu/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《线代数（第5版）》是一本经典线代数教材。此书深入浅出地展示了线代数的所有核心概念，讲述过程中恰当穿插了各种应用，体现了线代数*有用的思想。

线代数内容包括行列式、矩阵、线方程组与向量、矩阵的特征值与特征向量、二次型及Mathematica 软件的应用等。 每章都配有习题，书后给出了习题。本书在编写中力求重点突出、由浅入深、 通俗易懂，努力体现教学的适用。本书可作为高等院校工科专业的学生的教材，也可作为非数学类专业学生的教材或教学参考书。