LINEAR ALGEBRA AND LTS APPLICATIONSPDF电子书下载
- 电子书积分:16 积分如何计算积分?
- 作 者:DAVID C.LAY
- 出 版 社:ADDISON-WESLEY PUBLISHING COMPANY
- 出版年份:1993
- ISBN:
- 页数:508 页
1 SYSTEMS OF LINEAR EQUATIONS 1
Introductory Example:Linear Models in Economics and Engineering 1
1.1 Introduction to Systems of Linear Equations 2
1.2 Row Reduction and Echelon Forms 13
1.3 Applications of Linear Systems 25
Supplementary Exercises 34
2 VECTOR AND MATRIX EQUATIONS 37
Introductory Example:Nutrition Problems 37
2.1 Vectors in R” 38
2.2 The Equation Ax=b 48
2.3 Solution Sets of Linear Systems 56
2.4 Linear Independence 63
2.5 Introduction to Linear Transformations 71
2.6 The Matrix of a Linear Transformation 79
2.7 Applications to Nutrition and Population Movement 85
Supplementary Exercises 92
3 MATRIX ALGEBRA 95
Introductory Example:Computer Graphics in Automotive Design 95
3.1 Matrix Operations 96
3.2 The Inverse of a Matrix 107
3.3 Characterizations of Invertible Matrices 116
3.4 Partitioned Matrices 121
3.5 Matrix Factorizations 128
3.6 Iterative Solutions of Linear Systems 137
3.7 The Leontief Input-Output Model 142
3.8 Applications to Computer Graphics 148
Supplementary Exercises 158
4 DETERMINANTS 161
Introductory Example:Determinants in Analytic Geometry 161
4.1 Introduction to Determinants 162
4.2 Properties of Determinants 168
4.3 Cramer’s Rule,Volume,and Linear Transformations 176
Supplementary Exercises 186
5 VECTOR SPACES 189
Introductory Example:Space Flight and Control Systems 189
5.1 Vector Spaces and Subspaces 190
5.2 Null Spaces,Column Spaces,and Linear Transformations 200
5.3 Linearly Independent Sets; Bases 211
5.4 Coordinate Systems 219
5.5 The Dimension of a Vector Space 229
5.6 Rank 235
5.7 Change of Basis 243
5.8 Applications to Difference Equations 248
5.9 Applications to Markov Chains 259
Supplementary Exercises 269
6 EIGENVALUES AND EIGENVECTORS 271
Introductory Example:Dynamical Systems and Spotted Owls 271
6.1 Eigenvectors and Eigenvalues 273
6.2 The Characteristic Equation 280
6.3 Diagonalization 288
6.4 Eigenvectors and Linear Transformations 296
6.5 Complex Eigenvalues 303
6.6 Applications to Dynamical Systems 310
6.7 Iterative Estimates for Eigenvalues 321
Supplementary Exercises 329
7 ORTHOGONALITY AND LEAST-SQUARES 331
Introductory Example:Readjusting the North American Datum 331
7.1 Inner Product,Length,and Orthogonality 333
7.2 Orthogonal Sets 342
7.3 Orthogonal Projections 352
7.4 The Gram-Schmidt Process 359
7.5 Least-Squares Problems 366
7.6 Applications to Linear Models 376
7.7 Inner Product Spaces 384
7.8 Applications of Inner Product Spaces 393
Supplementary Exercises 401
8 SYMMETRIC MATRICES AND QUADRATIC FORMS 403
Introductory Example:Multichannel Image Processing 403
8.1 Diagonalization of Symmetric Matrices 405
8.2 Quadratic Forms 411
8.3 Constrained Optimization 419
8.4 The Singular Value Decomposition 426
8.5 Applications to Image Processing and Statistics 435
Supplementary Exercises 444
APPENDICES 447
A Uniqueness of the Reduced Echelon Form 447
B Complex Numbers 449
GLOSSARY 455
ANSWERS TO ODD-NUMBERED EXERCISES 467
- 《地球简史》(英)戴维·贝克(David Baker) 2020
- 《第三帝国的兴亡》(英)克里斯·毕晓普(Chris Bishop),(英)戴维·乔丹(David Jordan)著 2019
- 《图解轻武器史 剑、矛和锤》(美)大卫·苏德(David Soud)著;刘恒沙译 2017
- 《现代环境主义导论》(英)戴维·佩珀(David Pepper)著 2020
- 《中国经学史》(美)韩大伟(David B. Honey)著 2019
- 《火星生命 前往须知》(美)戴维·温特劳布(DAVID A. WEINTRAUB)著;傅承启译 2019
- 《程序员修炼之道 通向务实的最高境界 第2版》(美)David Thomas(大卫·托马斯),Andrew Hunt(安德鲁·亨特) 2020
- 《谁捉住了上帝粒子?》(法)大卫·卢阿普尔(David Louapre)著 2020
- 《博士生教育的变迁》(澳)大卫·鲍德(David Boud),(澳)艾莉森·李(Alison Lee)编 2019
- 《信息系统安全基础 原书第2版》(美)David Kim 2020
- 《非线性量子力学》庞小峰编著 2009
- 《爱与意志》(美)罗洛·梅著;冯川译 1998
- 《牛虻》(英)艾·丽·伏尼契著;亚贤译 1995
- 《自杀风险管理手册》(加)库奇,(加)切希尔著 2011
- 《柴油发动机系统设计》(美)辛千凡著;(美)辛千凡译 2015
- 《WIESEL骨科手术技巧 足踝外科》(美)Sam W. Wiesel总主编;(美)Mark E. Easley主编;张长青总主译 2015
- 《永续生活 16个家的创想物语》(日)意迪著;林叶,袁璟译 2014
- 《创伤骨科》(美)威塞尔主编;张长青总主译 2015
- 《WIESEL骨科手术技巧 成人重建外科》(美)威塞尔(Sam W. Wiesel)总主编;(美)Javad Parvizi,Richard H. Rothman主编;张长青总主译 2015
- 《结直肠癌规范化诊疗 国际进展与中国实践荟萃》陈功,邱萌,张俊主编;袁瑛,黄鼎智副主编 2015