线性代数导论

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

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