CHAPTER Ⅰ Vectors
1.Definition of Points in Space
2.Located Vectors
3.Scalar Product
4.The Norm of a Vector
5.Parametric Lines
6.Planes
CHAPTER Ⅱ Matrices and Linear Equations
1.Matrices
2.Multiplication of Matrices
3.Homogeneous Linear Equations and Elimination
4.Row Operations and Gauss Elimination
5.Row Operations and Elementary Matrices
6.Linear Combinations
CHAPTER Ⅲ Vector Spaces
1.Definitions
2.Linear Combinations
3.Convex Sets
4.Linear Independence
5.Dimension
6.The Rank of a Matrix
CHAPTER Ⅳ Linear Mappings
1.Mappings
2.Linear Mappings
3.The Kernel and Image of a Linear Map
4.The Rank and Linear Equations Again
5.The Matrix Associated with a Linear Map
Appendix: Change of Bases
CHAPTER Ⅴ Composition and Inverse Mappings
1.Composition of Linear Maps
2.Inverses
CHAPTER Ⅵ Scalar Products and Orthogonality
1.Scalar Products
2.Orthogonal Bases
3.Bilinear Maps and Matrices
CHAPTER Ⅶ Determinants
1.Determinants of Order 2
2.3×3 and n×n Determinants
3.The Rank of a Matrix and Subdeterminants
4.Cramer's Rule
5.Inverse of a Matrix
6.Determinants as Area and Volume
CHAPTER Ⅷ Eigenvectors and Eigenvalues
1.Eigenvectors and Eigenvalues
2.The Characteristic Polynomial
3.Eigenvalues and Eigenvectors of Symmetric Matrices
4.Diagonalization of a Symmetric Linear Map
Appendix Complex Numbers
Answers to Exercises
Index
· · · · · · (收起)