This book is meant as a short text in linear algebra for a one-term course. Except for an occasional example or exercise the text is logically independent of calculus, and could be taught early. In practice, I expect it to be used mostly for students who have had two or three terms of calculus. The course could also be given simultaneously with, or im mediately after, the first course in calculus.
目录
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 CHAPPTER 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 CHAPPTER V Composition and Inverse Mapping …… CHAPPTER Ⅵ Scalar Products and Orthogonlity CHAPPTER Ⅶ Determinants CHAPPTER Ⅷ Eigenvectors and Eigenvalues
