Linear algebra with applications ( 线性代数)
发布日期:2007-09-05 浏览次
[内容简介]
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子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。.?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。本书主要特点?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。
[目次]
PREFACE.
1MATRICES AND SYSTEMS OF EQUATIONS
1 Systems of Linear Equations
2 Row Echelon Form
3 Matrix Algebra
4 Elementary Matrices
5 Partitioned Matrices
MATLAB Exercises
Chapter Test A
Chapter Test B
2 DETERMINANTS
1 The Determinant of a Matrix
2 Properties of Determinants
3 Cramer's Rule
MATLAB Exercises
Chapter Test A
Chapter Test B
3 VECTOR SPACES
1 Definition and Examples
2 Subspaces
3 Linear Independence
4 Basis and Dimension
5 Change of Basis
6 Row Space and Column Space
MATLAB Exercises
Chapter Test A
Chapter Test B
4 LINEAR TRANSFORMATIONS
1 Definition and Examples
2 Matrix Representations of Linear Transformations
3 Similarity
MATLAB Exercises
Chapter Test A
Chapter Test B
5 ORTHOGONALITY
1 The Scalar Product in Rn
2 Orthogonal Subspaces
3 Least Squares Problems
4 Inner Product Spaces
5 Orthonormal Sets
6 The Gram-Schmidt Orthogonalization Process
7 Orthogonal Polynomials
MATLAB Exercises
Chapter Test A
Chapter Test B
6 EIGENVALUES
1 Eigenvalues and Eigenvectors
2 Systems of Linear Differential Equations
3 Diagonalization
4 Hermitian Matrices
5 The Singular Value Decomposition
G Quadrati Forms
7 Positive Definite Matrices
8 Nonnegative Matrices
MATLAB Exercises
Chapter Test A
Chapter Test B
7 NUMERICAL LINEAR ALGEBRA
1 Floating-Point Numbers
2 Gaussian Elimination
3 Pivoting Strategies
4 Matrix Norms and Condition Numbers
5 Orthogonal Transformations
6 The Eigenvalue Problem
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
【关闭】
新书报道