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。本书作者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。
本书主要特点
? 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。

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

Steven J. Leon 1971年于密歇根州立大学数学系获得博士学位,现为马萨诸塞大学达特茅斯分校数学系**教授,ILAS(国际线性代数协会)、MAA(美国数学学会)和SIAM(美国工业与应用数学协会)成员。他主要从事科学计算、线性代数和应用数学等领域的研究。