線性代數(shù)引論

內(nèi)容概要

　　《線性代數(shù)引論》內(nèi)容覆蓋了我國現(xiàn)行理工科大學線性代數(shù)課程的全部內(nèi)容，與我國現(xiàn)行的線性代數(shù)教學大綱和教材體系比較接近。其中包括矩陣與線性方程組、二維和三維空間、向量空間R、特征值問題、向量空間和線性交換、行列式、特征值及其應(yīng)用等?！毒€性代數(shù)引論》的編寫采用模塊式結(jié)構(gòu)，便于廣大教師根據(jù)教學需要對內(nèi)容進行取舍?！毒€性代數(shù)引論》通過例子介紹了非常流行的教學軟件Matlab在線性代數(shù)中的應(yīng)用，并且每章結(jié)尾都附有專門用Matlab做的練習題?！毒€性代數(shù)引論》可供理工科、經(jīng)濟管理各專業(yè)學生作為教科書或參考書，也可供科技人員和自學者參考。

作者簡介

作者：(美國)李 W·約翰遜(Lee W.Johnsom) (美國)R·迪安 里斯(R.Dean Riess) (美國)吉米 T·阿諾德(Jimmy T.Arnold)

書籍目錄

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

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