线性代数(第5版)
作 者:[美]Gilbert Strang 吉尔伯特·斯特朗) 著
定 价:108
出 版 社:清华大学出版社
出版日期:2019年08月01日
页 数:0
装 帧:简装
ISBN:9787302535560
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。
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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
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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