线性代数

preface

matrices and systems of equations

1.1 systems of linear equations

1.2 row echelonform

1.3 matrix arithmetic

1.4 matrix algebra

1.5 elementary matrices

1.6 partitioned matrices

matlab r exercises

chaptertesta

chaptertestb

2 determinants

2.1 the determinant of a matrix

2.2 properties of determinants

2.3. additionaltopics and applications

matlab exercises

chaptertesta

chaptertestb

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

chaptertesta

chaptertestb

4 linear transformations

4.1 definition and examples

4.2 matrix representationsof lineartransformations

4.3 similarity

matlab exercises

chaptertesta

chaptertestb

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

chaptertesta

chaptertestb

6 eigenvalues

6.1 eigenvalues and eigenvectors

6.2 systems of linear differential equations

6.3 diagonalization

6.4 hermitian matrices

6.5 the singularvalue decomposition

6.6 quadraticforms

6.7 positive definite matrices

6.8 nonnegative matrices

matlab exercises

chaptertesta

chaptertestb

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 web.

9 canonical forms web.

appendix: matlab

bibliography

answers to selected exercises

index

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　　在第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。

　　《线性代数（英文版第8版）》主要特点：

　　理论与应用有机结合。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。

　　示例丰富。便于读者理解相关的定义及原理，增强了读者学习的兴趣。

　　习题安排错落有致。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。

　　紧密结合数学工具MATLAB。每章的后面都有基于MATLAB的上机练习，并在附录中介绍了MATLAB的基本用法。