线性代数(第5版)

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，体现了线性代数特别有用的思想。

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。

"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。 "

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