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.

此书为英文版。

CHAPTER I

Vectors

1. Definition of Poinls 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

. Linear Independence

5. Dimension

6. The Rank cf 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 x 3 and n x 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

Eigenveetors 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