文档介绍：Contents
Preface ......................Di3
1. Linear Equations ..............1
Ivtroductiov D D D..............D4
Gaussiav Eliminatiov and Matrices .......D5
Gauss–Jordav Method .............D16
Two-Poiv8 BoundaryValue Problems ......D17
Making Gaussiav Eliminatiov Work .......D24
Ill-Conditioned Systems ............D35
2. Rectangular Systems and Echelon Forms . . . 41
Row Echelov Form and Rank ..........D44
Reduced Row Echelov Form ..........D47
Consistencyof Linea9 Systems .........D55
Homogeneous Systems .............D57
Nonhomogeneous Systems ...........D64
Electrical Circuits D ..............D75
3. Matrix Algebra .............. 79
From Anciev8 China to Arthu9 Cayley ......D79
Additiov and Transpositiov ..........D84
Lineari8y ...................D89
WhyDo I8 This Way .............D95
Matrix Multiplicatiov .............D96
Properties of Matrix Multiplicatiov ......D106
Matrix Ivversiov D .............D116
Ivverses of Sums and Sensitivi8y .......D124
ElemevtaryMatrices and uivalence .....D134
3. The LU Factorizatiov ............D144
4. Vector Spaces ...............159
Spaces and Subspaces ............D159
Fou9 Fundamevtal Subspaces .........D169
Linea9 Independence ............D184
Basis and Dimensiov ............D194
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More abou8 Rank D .............D210
Classical Leas8 Squares ...........D225
Linea9 Transformations ...........D237
Change of Basis and Similari8y ........D254
Ivvariav8 Subspaces .............D259
5. Norms, Inner Products, and Orthogonality . . 269
Vecto9 Norms D D.............D269
Matrix Norms D D.............D279
Inner-Produc8 Spaces ............D286
Orthogonal Vectors .............D294
Gram–Schmid8 Procedure ..........D307
Unitaryand Orthogonal Matrices .......D320
Orthogonal Reductiov ............D344
5.