线性代数引论

出版时间：2012-7  出版社：机工  作者：约翰逊  页数：555  字数：967000  
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内容概要

　　《线性代数引论》内容覆盖了我国现行理工科大学线性代数课程的全部内容，与我国现行的线性代数教学大纲和教材体系比较接近。其中包括矩阵与线性方程组、二维和三维空间、向量空间R、特征值问题、向量空间和线性交换、行列式、特征值及其应用等。《线性代数引论》的编写采用模块式结构，便于广大教师根据教学需要对内容进行取舍。《线性代数引论》通过例子介绍了非常流行的教学软件Matlab在线性代数中的应用，并且每章结尾都附有专门用Matlab做的练习题。《线性代数引论》可供理工科、经济管理各专业学生作为教科书或参考书，也可供科技人员和自学者参考。

作者简介

作者：(美国)李 W·约翰逊(Lee W.Johnsom) (美国)R·迪安 里斯(R.Dean Riess) (美国)吉米 T·阿诺德(Jimmy T.Arnold)

书籍目录

1 MATRICES AND SYSTEMS OF LINEAR EQUATIONS
1.1 Introduction to Matrices and Systems of Linear Equations
1.2 Echelon Form and Gauss-Jordan Elimination
1.3 Consistent Systems of Linear Equations
1.4 Applications (Optional)
1.5 Matrix Operations
1.6 Algebraic Propertiesof Matrix Operations
1.7 Linear Independence and Nonsingular Matrices
1.8 Data Fitting, Numerical Integration, and Numerical
Differentiation (Optional)
1.9 Matrix Inverses and Their Properties
2 VECTORS IN 2-SPACE AND 3-SPACE
2.1 Vectors in the Plane
2.2 Vectors in Space
2.3 The Dot Product and the Cross Product
2.4 Lines and Planes in Space
3 THE VECTOR SPACE Rn
3.1 Introduction
3.2 Vector Space Properties of Rn
3.3 Examples of Subspaces
3.4 Bases for Subspaces
3.5 Dimension
3.6 Orthogonal Bases for Subspaces
3.7 Linear Transformations from Rn to Rm
3.8 Least-Squares Solutions to Inconsistent Systems, with
Applications to Data Fitting
3.9 Theory and Practice of Least Squares
4 THE EIGENVALUE PROBLEM
4.1 The Eigenvalue Problem for (2 x 2) Matrices
4.2 Determinants and the Eigenvalue Problem
4.3 Elementary Operations and Determinants (Optional)
4.4 Eigenvalues and the Characteristic Polynomial
4.5 Eigenvectors and Eigenspaces
4.6 Complex Eigenvalues and Eigenvectors
4.7 Similarity Transformations and Diagonalization
4.8 Difference Equations; Markov Chains; Systems of Differential
Equations (Optional)
5 VECTOR SPACES AND LINEAR TRANSFORMATIONS
5.1 Introduction
5.2 Vector Spaces
5.3 Subspaces
5.4 Linear Independence, Bases, and Coordinates
5.5 Dimension
5.6 Inner-Product Spaces, Orthogonal Bases, and Projections
(Optional)
5.7 Linear Transformations
5.8 Operations with Linear Transformations
5.9 Matrix Representations for Linear Transformations
5.10 Change of Basis and Diagonalization
6.DETERMINANTS
6.1 Introduction
6.2 Cofactor Expansions of Determinants
6.3 Elementary Operations and Determinants
6.4 Cramers Rule
6.5 Applications of Determinants: Inverses and Wronksians
7.EIGENVALUES AND APPLICATIONS
7.1 Quadratic Forms
7.2 Systems of Differential Equations
7.3 Transformation to Hessenberg Form
7.4 Eigenvalues of Hessenberg Matrices
7.5 Householder Transformations
7.6 The QR Factorization and Least-Squares Solutions
7.7 Matrix Polynomials and the Cayley-Hamilton Theorem
7.8 Generalized Eigenvectors and Solutions of Systems of
Differential Equations
APPENDIX: AN INTRODUCTION TO MATLAB
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
INDEX

用户评论 (总计12条)

•   非常好，講得很清楚，目前還沒有發現錯誤
•   挺难的 不好懂
•   应该是很好的一本书，只不过发错版次了。本来想换的，结果直接给退货了，只好重新买了。快递不错。
•   MIT的那个教材是Gilbert Strang编写的。也叫《Introduction to Linear Algebra》
•   很好，由浅入深，切换的很自然不想国内教材那么突兀
•   各位，看看人家老外的书，这才叫教材，循序渐进，由易到难，把问题讲的清清楚楚，明明白白，看这种书真是一种享受，其乐无穷啊，国内编的那是教材吗？？那种书能把人教明白吗？？国产教材充其量称之为“备忘录”。强烈推荐看英文教材，一个字，好！！
•   因为线性代数课采用英文教学，我们老师选定这本教材，她说很经典，研究生都可以用。但是中文的线性代数教材比英文的简洁。
•   不错的书，学Matrix Algebra很有用
•   正品，内容也不错，需要查的单词也不多，适合本科生阅读
•   学习线代的必备书。强烈推荐啊
•   good 很详细 很不错
•   和网易公开课的MIT线性代数配套 买来看看 那老头讲的也好 书写的也好