出版社:清華大學出版社 ISBN:9787302535560 商品編碼:56291303765 品牌:文軒 出版時間:2019-08-01 代碼:108 作者:GilbertStrang吉爾伯特·斯特朗)
" 作 者:[美]Gilbert Strang 吉爾伯特·斯特朗) 著 定 價:108 出 版 社:清華大學出版社 出版日期:2019年08月01日 頁 數:0 裝 幀:簡裝 ISBN:9787302535560 Gilbert Strang的《線性代數(第5版)》是一本經典線性代數教材。此書深入淺出地展示了線性代數的所有核心概念,講述過程中恰當穿插了各種應用,體現了線性代數特別有用的思想。 ●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 itiveDe 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 ltivariate Gaussian and Weighted Least Squares 554 MatrixFactorizations 562 Index 564 SixGreatTheorems/LinearAlgebrain aNutshell 573 線性代數內容包括行列式、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 軟件的應用等。 每章都配有習題,書後給出了習題答案。本書在編寫中力求重點突出、由淺入深、 通俗易懂,努力體現教學的適用性。本書可作為高等院校工科專業的學生的教材,也可作為其他非數學類本科專業學生的教材或教學參考書。 [美]Gilbert Strang 吉爾伯特·斯特朗) 著 "作者GILBERT STRANG為Massachusetts Institute of Technology數學繫教授。從UCLA博士畢業後一直在MIT任教.教授的課程有“數據分析的矩陣方法”“線性代數”“計算機科學與工程”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 等 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 MIT’s 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 prepa等
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