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，现代软件技术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。

　　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。
　　● 习题安排科学合理。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MALAB的上机练习，并在附录中介绍了MALAB的基本用法。

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1. Matrices and Systems of Equations.

Systems of Linear Equations. Row Echelon Form. Matrix Algebra. Elementary Matrices. Partitioned Matrices. Matlab Exercises. Chapter Test.



2. Determinants.

The Determinant of a Matrix. Properties of Determinants. Cramer's Rule. Matlab Exercises. Chapter Test.



3. Vector Spaces.

Definition and Examples. Subspaces. Linear Independence. Basis and Dimension. Change of Basis. Row Space and Column Space. Matlab Exercises. Chapter Test.



4. Linear Transformations.

Definition and Examples. Matrix Representations of Linear Transformations. Similarity. Matlab Exercises. Chapter Test.



5. Orthogonality.

The Scalar Product in Rn. Orthogonal Subspaces. Least Squares Problems. Inner Product Spaces. Orthonormal Sets. The Gram-Schmidt Orthogonalization Process. Orthogonal Polynomials. Matlab Exercises. Chapter Test.



6. Eigenvalues.

Eigenvalues and Eigenvectors. Systems of Linear Differential Equations. Diagonalization. Hermitian Matrices. The Singular Value Decomposition. Quadratic Forms. Positive Definite Matrices. Nonnegative Matrices. Matlab Exercises. Chapter Test.



7. Numerical Linear Algebra.

Floating-Point Numbers. Gaussian Elimination. Pivoting Strategies. Matrix Norms and Condition Numbers. Orthogonal Transformations. The Eigenvalue Problem. Least Squares Problems. Matlab Exercises. Chapter Test.



8. Iterative Methods. On the website, as pdfs.



9. Jordan Canonical Form. On the website, as pdfs.



Appendix: MATLAB.



Bibliography.



Answers to Selected Exercises.



Index.