《线性代数(英文版第8版)》(作者利昂)的大量的实际应用贯穿于理论讲解的始终，体现了线性代数在各个领域中的广泛应用。本书便于读者理解相关的定义及原理，增强了读者学习的兴趣。书中每一节的后面给出大量的习题，各章后面还有测试题，使学生有更多的演练机会，达到触类旁通的效果。

随着计算机技术的发展，线性代数课程的重要性越来越突出。同时，现代软件已经为显著改进授课方式提供了可能。《线性代数(英文版第8版)》作者利昂多年讲授线性代数课程，并在教学过程中不断探索更利于学生理解的新教学方法，从而使本书更加适合作为线性代数课程的教材。

在《线性代数(英文版第8版)》中，扩充了矩阵代数的知识，新增了向量积、实舒尔分解的内容，并增加了130多道新练习。

Preface

1 Matrices and Systems of Equations

1.1 Systems of Linear Equations

1.2 Row Echelon Form

1.3 Matrix Arithmetic

1.4 Matrix Algebra

1.5 Elementary Matrices

1.6 Partitioned Matrices

MATLAB Exercises

Chapter Test A

Chapter Test B

2 Determinants

2.1 The Detemainant of, a Matrix

2.2 Properties of Determinants

2.3 Additional Topics and Applications

MATLAB Exercises

Chapter Test A

Chapter Test B

3 Vector Spaces

3.1 Definition and Examples

3.2 Subspaces

3.3 Linear Independence

3.4 Basis and Dimension

3.5 Change of Basis

3.6 Row Space and Column Space

MATLAB Exercises

Chapter Test A

Chapter Test B

4 Linear Transformations

4.1 Definition and Examples

4.2 Matrix Representations of Linear Transformations

4.3 Similarity

MATLAB Exercises

Chapter Test A

Chapter Test B

5 Orthogonality

5.1 The Scalar Product in Rn

5.2 Orthogonal Subspaces

5.3 Least Squares Problems

5.4 Inner Product Spaces

5.5 Orthonormal Sets

5.6 The Gram-Schmidt Orthogonalization Process

5.7 Orthogonal Polynomials

MATLAB Exercises

Chapter Test A

Chapter Test B

6 Eigenvalues

6.1 Eigenvalues and Eigenvectors

6.2 Systems of Linear Differential Equations

6.3 Diagonalization

6.4 Hermitian Matrices

6.5 The Singular Value Decomposition

6.6 Quadratic Forms

6.7 Positive Definite Matrices

6.8 Nonnegative Matrices

MATLAB Exercises

Chapter Test A

Chapter Test B

7 Numerical Linear Algebra

7.1 Floating-Point Numbers

7.2 Gaussian Elimination

7.3 Pivoting Strategies

7.4 Matrix Norms and Condition Numbers

7.5 Orthogonal Transformations

7.6 The Eigenvalue Problem

7.7 Least Squares Problems

MATLAB Exercises

Chapter Test A

Chapter Test B

8 Iterative Methods

9 Canonical Forms

Appendix: MATLAB

Bibliography

Answers to Selected Exercises

Index