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Introduction to Linear Algebra （第五版）PDF|Epub|txt|kindle电子书版本网盘下载
- [美]李 W.约翰逊（Lee W.Johnson) R.迪安 里斯（R.Dean Riess） 吉米 T.阿诺德（Jimmy T.Amold）著 著
- 出版社： 机械工业出版社
- ISBN：
- 出版时间：2003
- 标注页数：555页
- 文件大小：87MB
- 文件页数：615页
- 主题词：
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图书目录
1.MATRICES AND SYSTEMS OF LINEAR EQUATIONS1
1.1 Introduction to Matrices and Systems of Linear Equations2
1.2 Echelon Form and Gauss-Jordan Elimination14
1.3 Consistent Systems of Linear Equations28
1.4 Applications（Optional）39
1.5 Matrix Operations46
1.6 Algebraic Properties of Matrix Operations61
1.7 Linear Independence and Nonsingular Matrices71
1.8 Data Fitting, Numerical Integration, and Numerical Differentiation （Optional）80
1.9 Matrix Inverses and Their Properties92
2.VECTORS IN 2-SPACE AND 3-SPACE113
2.1 Vectors in the Plane114
2.2 Vectors in Space128
2.3 The Dot Product and the Cross Product135
2.4 Lines and Planes in Space148
3.THE VECTOR SPACE Rn163
3.1 Introduction164
3.2 Vector Space Properties of Rn167
3.3 Examples of Subspaces176
3.4 Bases for Subspaces188
3.5 Dimension202
3.6 Orthogonal Bases for Subspaces214
3.7 Linear Transformations from Rn to Rm225
3.8 Least-Squares Solutions to Inconsistent Systems,with Applications to Data Fitting243
3.9 Theory and Practice of Least Squares255
4.THE EIGENVALUE PROBLEM275
4.1 The Eigenvalue Problem for （2×2） Matrices276
4.2 Determinants and the Eigenvalue Problem280
4.3 Elementary Operations and Determinants （Optional）290
4.4 Eigenvalues and the Characteristic Polynomial298
4.5 Eigenvectorsand Eigenspaces307
4.6 Complex Eigenvalues and Eigenvectors315
4.7 Similarity Transformations and Diagonalization325
4.8 Difference Equations; Markov Chains; Systems of Differential Equations （Optional）338
5.VECTOR SPACES AND LINEAR TRANSFORMATIONS357
5.1 Introduction358
5.2 Vector Spaces360
5.3 Subspaces368
5.4 Linear Independence, Bases, and Coordinates375
5.5 Dimension388
5.6 Inner-Product Spaces, Orthogonal Bases, and Projections （Optional）392
5.7 Linear Transformations403
5.8 Operations with Linear Transformations411
5.9 Matrix Representations for Linear Transformations419
5.10 Change of Basis and Diagonalization431
6.DETERMINANTS447
6.1 Introduction448
6.2 Cofactor Expansions of Determinants448
6.3 Elementa Operations and Determinants455
6.4 Cramer's Rule465
6.5 Applications of Determinants:Inverses and Wronksians471
7.EIGENVALUES AND APPLICATIONS483
7.1 Quadratic Forms484
7.2 Systems of Differential Equations493
7.3 Transformation to Hessenberg Form502
7.4 Eigenvalues of Hessenberg Matrices510
7.5 Householder Transformations519
7.6 The QR Factorization and Least-Squares Solutions531
7.7 Matrix Polynomials and the Cayley-Hamilton Theorem540
7.8 Generalized Eigenvectors and Solutions of Systemsof Differential Equations546