文档介绍：Contents
Preface .......................ix
1. Linear Equations ..............1
Introduction . . . ............... 1
Gaussian Elimination and Matrices ........ 3
Gauss–Jordan Method ..............15
Two-Point BoundaryValue Problems .......18
Making Gaussian Elimination Work ........21
Ill-Conditioned Systems .............33
2. Rectangular Systems and Echelon Forms . . . 41
Row Echelon Form and Rank ...........41
Reduced Row Echelon Form ...........47
Consistencyof Linear Systems ..........53
Homogeneous Systems ..............57
Nonhomogeneous Systems ............64
Electrical Circuits . ...............73
3. Matrix Algebra .............. 79
From Ancient China to Arthur Cayley .......79
Addition and Transposition ...........81
Linearity ....................89
WhyDo It This Way ..............93
Matrix Multiplication ..............95
Properties of Matrix Multiplication ....... 105
Matrix Inversion . .............. 115
Inverses of Sums and Sensitivity ........ 124
ElementaryMatrices and Equivalence ...... 131
The LU Factorization ............. 141
4. Vector Spaces ...............159
Spaces and Subspaces ............. 159
Four Fundamental Subspaces .......... 169
Linear Independence ............. 181
Basis and Dimension ............. 194
vi Contents
More about Rank . .............. 210
Classical Least Squares ............ 223
Linear Transformations ............ 238
Change of Basis and Similarity ......... 251
Invariant Subspaces .............. 259
5. Norms, Inner Products, and Orthogonality . . 269
Vector Norms . . .............. 269
Matrix Norms . . .............. 279
Inner-Product Spaces ............. 286
Orthogonal Vectors .............. 294
Gram–Schmidt Procedure ........... 307
Unitaryand Orthogonal Matrices ........ 320
Orthogonal Re