線性代數(shù)（第5版）

定　價：￥108.00

作　者：	[美] Gilbert Strang 著
出版社：	清華大學(xué)出版社
叢編項：
標(biāo)　簽：	暫缺

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ISBN：	9787302535560	出版時間：	2019-08-01	包裝：	平裝
開本：	16開	頁數(shù)：	573	字?jǐn)?shù)：

內(nèi)容簡介

　　線性代數(shù)內(nèi)容包括行列式、矩陣、線性方程組與向量、矩陣的特征值與特征向量、二次型及Mathematica 軟件的應(yīng)用等。每章都配有習(xí)題，書后給出了習(xí)題答案。本書在編寫中力求重點突出、由淺入深、通俗易懂，努力體現(xiàn)教學(xué)的適用性。本書可作為高等院校工科專業(yè)的學(xué)生的教材，也可作為其他非數(shù)學(xué)類本科專業(yè)學(xué)生的教材或教學(xué)參考書。

作者簡介

　　作者GILBERT STRANG為Massachusetts Institute of Technology數(shù)學(xué)系教授。從UCLA博士畢業(yè)后一直在MIT任教.教授的課程有“數(shù)據(jù)分析的矩陣方法”“線性代數(shù)”“計算機(jī)科學(xué)與工程”等，出版的圖書有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。

圖書目錄

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