内容提要
《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。
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, andNumericalDifferentiation (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,withApplications 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 ofDifferentialEquations (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, andProjections(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 SystemsofDifferential Equations
APPENDIX: AN INTRODUCTION TO MATLAB
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
INDEX
