本书用英语写成，包含多项式和线性代数的基本内容，主要包括：整数和多项式，线性方程组，线性映射，矩阵和行列式，线性空间和线性映射，线性变换等。本书适合数学系本科生作为高等代数教材使用，也可作为双语教学和线性代数的参考教材。

本书用英语写成，包含多项式和线性代数的基本内容，逻辑清晰，章节安排自然合理，有近550道配套习题，许多习题十分新颖。主要内容包括：整数和多项式，线性方程组，线性映射，矩阵和行列式，线性空间和线性映射，线性变换，欧几里得空间，线性型，双线性型以及二次型。本书适合数学系本科生作为高等代数教材使用，也可作为双语教学和线性代数的参考教材。

1 Integers and Polynomials

1.1 Integers 

1.2 N'umber Fields

1.3 Polynomial

1.4 Polynomial Functions and Roots

1.5 Polvnomials over Rational Number Field

1.6 Polynomials of Several Variables

1.7 Symmetric Polynomials

1.8 Exercises

2 Systems of Linear Equations

2.1 Systems of Linear Equations and Elimination 

2.2 Vectors 

2.3 Matrices

2.4 Structure of Solutions of A System of Linear Equations

2.5 Exercises

3 Linear Maps, Matrices and Determinants

3. 1 Linear Maps of Vector Spaces and Matrices 

3.2 Operations of Linear Maps and Matrices

3.3 Partitioned Matrices

3, 4 Elementary Matrices and Invertible Matrices

3.5 Determinants

3.5.1 Permutation and Determinant

3.5.2 Properties of Determinant

3.5.3 Expansion of Determinant

3.5.4 Applications of Determinant

3.6 Exercises

4 Linear Spaces and Linear Maps

4. 1 Linear Spaces

4.2 Dimension, Basis, Coordinates

4.3 Basis Change and Coordinate Transformations

4.4 Linear Maps and Isomorphism

4.5 Matrices of Linear Maps

4.6 Subspaces and Direct Sum

4.7 Space Decomposition and Partitioned Matrices

4.8 Exercises

5 Linear Transformations

5.1 Linear Transformations

5.2 Similarity of Matrices

5.3 ),-Matrices

5.4 Eigenvalues, Eigenvectors and Characteristic Polynomials

5.5 Invariant Subspaces

5.6 Equivalence of λ-matrices

5.7 Invariant Factors and Elementary Divisors

5.8 Condition for Similarity of Matrices

5.9 Jordan Canonical Forms of Matrices

5.10 Rat iona! Canonical Forms of Matrices

5.11 Exercises

6 Euclidean Spaces

6.1 Inner Product and Basic Properties

6.2 Orthogonal Bases and Schmidt Orthonormalization

6.3 Subspaces and Orthogonal Complements

6.4 Isometry and Orthogonal Transformations

6.5 Symmetric Matrices and Symmetric Transformations 

6.6 The Method of Least Squares--System of Linear Equations

Revisited

6.7 A Brief Introduction to Unitary Spaces

6.8 Exercises

7 Linear Forms, Bilinear Forms and Quadratic Forms

7.1 Linear Forms and the Dual Space

7.2 Bilinear Forms

7.3 Symmetric Bilinear Forms

7.4 Quadratic Forms

7.5 Quadratic Forms over Real and Complex Number Fields

7.6 Positive Definite Quadratic Forms over Real Number Field

7.7 Exercises

Bibliography

Index