文件名称：Gilbert_Strang-Linear_Algebra_and_Its_Applications_4ed
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更新时间：2013-10-14 03:45:19
Linear Algebra and Its Applications
Contents Preface iv 1 Matrices and Gaussian Elimination 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Geometry of Linear Equations . . . . . . . . . . . . . . . . . . . . 4 1.3 An Example of Gaussian Elimination . . . . . . . . . . . . . . . . . . 13 1.4 Matrix Notation and Matrix Multiplication . . . . . . . . . . . . . . . . 21 1.5 Triangular Factors and Row Exchanges . . . . . . . . . . . . . . . . . 36 1.6 Inverses and Transposes . . . . . . . . . . . . . . . . . . . . . . . . . . 50 1.7 Special Matrices and Applications . . . . . . . . . . . . . . . . . . . . 66 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2 Vector Spaces 77 2.1 Vector Spaces and Subspaces . . . . . . . . . . . . . . . . . . . . . . . 77 2.2 Solving Ax = 0 and Ax = b . . . . . . . . . . . . . . . . . . . . . . . . 86 2.3 Linear Independence, Basis, and Dimension . . . . . . . . . . . . . . . 103 2.4 The Four Fundamental Subspaces . . . . . . . . . . . . . . . . . . . . 115 2.5 Graphs and Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 2.6 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 3 Orthogonality 159 3.1 Orthogonal Vectors and Subspaces . . . . . . . . . . . . . . . . . . . . 159 3.2 Cosines and Projections onto Lines . . . . . . . . . . . . . . . . . . . . 171 3.3 Projections and Least Squares . . . . . . . . . . . . . . . . . . . . . . 180 3.4 Orthogonal Bases and Gram-Schmidt . . . . . . . . . . . . . . . . . . 195 3.5 The Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . 211 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 i