Introduction to Linear Algebra, 5/e
內容描述
線性代數內容包括行列式、矩陣、線性方程組與向量、矩陣的特徵值與特徵向量、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。
目錄大綱
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
作者介紹
作者GILBERT STRANG為Massachusetts Institute of Technology數學系教授。
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 Books and Articles、Differential Equations and Linear Algebra。
_@9789574997947_https://static.coderbridge.com/images/books/9789574997947.jpg)
_@9780692196380_https://static.coderbridge.com/images/books/9780692196380.jpg)