线性代数（第5版）

定　　价：108 元

• 作者：[美]Gilbert Strang (吉尔伯特·斯特朗）
• 出版时间：2019/8/1
• ISBN：9787302535560
• 出 版 社：清华大学出版社

• 中图法分类：O151.2 
• 纸张：胶版纸
• 开本：16开

内容简介

线性代数内容包括行列式、矩阵、线性方程组与向量、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，书后给出了习题答案。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性。本书可作为高等院校工科专业的学生的教材，也可作为其他非数学类本科专业学生的教材或教学参考书。

编辑推荐

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*有用的思想。

序 言

Preface

I am happy for you to see this Fifth Edition of Introduction to Linear Algebra. This is the text for my video lectures on MITs OpenCourseWare (ocw.mit.edu and also YouTube). I hope those lectures will be useful to you (maybe even enjoyable !).
Hundreds of colleges and universities have chosen this textbook for their basic linear algebra course. A sabbatical gave me a chance to prepare two new chapters about probability and statistics and understanding data. Thousands of other improvements too probably only noticed by the author. . . Here is a new addition for students and all readers:
Every section opens with a brief summary to explain its contents. When you read a new section, and when you revisit a section to review and organize it in your mind, those lines are a quick guide and an aid to memory.
Another big change comes on this books website math.mit.edu/linearalgebra. That site now contains solutions to the Problem Sets in the book. With unlimited space, this is much more .exible than printing short solutions. There are three key websites :
ocw.mit.edu Messages come from thousands of students and faculty about linear algebra on this OpenCourseWare site. The 18.06 and 18.06 SC courses include video lectures of a complete semester of classes. Those lectures offer an independent review of the whole subject based on this textbookthe professors time stays free and the students time can be 2 a.m. (The reader doesnt have to be in a class at all.) Six million viewers around the world have seen these videos (amazing). I hope you .nd them helpful.
web.mit.edu/18.06 This site has homeworks and exams (with solutions) for the current course as it is taught, and as far back as 1996. There are also review questions, Java demos, Teaching Codes, and short essays (and the video lectures). My goal is to make this book as useful to you as possible, with all the course material we can provide.
math.mit.edu/linearalgebra This has become an active website. It now has Solutions to Exerciseswith space to explain ideas. There are also new exercises from many dif-ferent sourcespractice problems, development of textbook examples, codes in MATLAB and Julia and Python, plus whole collections of exams (18.06 and others) for review.
Please visit this linear algebra site. Send suggestions to [e-mail]

作者介绍

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 [e-mail]、Complete List of Books and Articles、Differential Equations and Linear Algebra。

目 录

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 CramersRule,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