自动控制中的线性代数 英文PDF电子书下载
- 电子书积分:12 积分如何计算积分?
- 作 者:伍清河编著
- 出 版 社:北京:国防工业出版社
- 出版年份:2011
- ISBN:9787118079012
- 页数:348 页
Chapter 1 Linear Space and Mapping 1
1.1 Some Basic Concepts of Abstract Algebra 1
1.1.1 Algebraic Systems 1
1.1.2 Groups 1
1.1.3 Rings 5
1.1.4 Fields 6
1.2 Linear Spaces 7
1.2.1 The Basic Concepts 7
1.2.2 Linear Dependency 9
1.3 Basis of a Linear Space 10
1.3.1 The Notion of a Basis 10
1.3.2 Change of Basis and Transition Matrices 12
1.4 Linear Subspaces 15
1.4.1 The Notion of Linear Subspace 15
1.4.2 Sum and Intersect of Subspaces 16
1.4.3 Direct Sum and Complementary Subspace 20
1.5 Linear Transformations 21
1.5.1 Notion of a Linear Transformation 21
1.5.2 The Matrix Representation of a Linear Transformation 23
1.5.3 Isomorphism on Finite Dimensional Linear Spaces 29
1.5.4 Range and Kernel of a Linear Transformation 30
1.5.5 Composite Transformation 33
1.6 Quotient Space 34
1.6.1 Quotient Space 34
1.6.2 Regular Projection and Induced Transformation 42
1.7 Notes and References 45
1.8 Exercises and Problems 45
Chapter 2 Polynomials and Matrix Polynomials 48
2.1 Linear Algebras 48
2.2 Ring and Euclidean Division 52
2.3 Ideals of Polynomials 56
2.4 Factorization of a Polynomial 60
2.5 Matrix Polynomials 64
2.6 Unimodular λ-Matrix and the Smith Canonical Form 65
2.7 Eleinentary Divisors and Equivalence of Matrix Polynomials 75
2.8 Ideal of Matrix Polynomials and Coprimeness 82
2.9 Notes and References 83
2.10 Problems and Exercises 84
Chapter 3 Linear Transformations 86
3.1 The Eigenvalues of a Linear Transformation 86
3.2 Similarity Reduction,Conditions on Similarity and the Natural Normal Form 93
3.2.1 Conditions on Similarity 93
3.2.2 Similarity Reduction and the Natural Normal Form 95
3.3 The Jordan Canonical Forms in Cn×n and Rn×n 100
3.3.1 The Jordan Canonical Forms in Cn×n 100
3.3.2 The Jordan Canonical Forms in Rn×n 103
3.3.3 The Transition Matrix X 105
3.3.4 Decomposing V into the Direct Sum of Jordan Subspaces 113
3.4 Minimal Polynomials and the First Decomposition of a Linear Space 116
3.4.1 Annihilating and Minimal Polynomials 116
3.4.2 The First Decomposition of a Linear Space 118
3.4.3 Decomposition of a Linear Space V over the Field C 121
3.5 The Cyclic Invariant Subspaces and the Second Decomposition of a Linear Space 125
3.5.1 The Notion of a Cyclic Invariant Subspace 125
3.5.2 The Second Decomposition of a Linear Space 126
3.5.3 Illustrating Examples 129
3.6 Notes and Reference 133
3.7 Problems and Exercises 134
Chapter 4 Linear Transformations in Unitary Spaces 136
4.1 Euclidean and Unitary Spaces 136
4.1.1 The Notions of Euclidean and Unitary Spaces 136
4.1.2 The Characteristics of a Unitary Space 138
4.1.3 The Metric in Unitary Spaces 140
4.2 Orthonormal Basis and the Gram-Schmidt Process 142
4.3 Unitary Transformations 147
4.4 Projectors and Idempotent Matrices 150
4.4.1 Projectors and Idempotent Matrices 150
4.4.2 Orthogonal Complement and Orthogonal Projectors 154
4.5 Adjoint Transformation 156
4.6 Normal Transformations and Normal Matrices 158
4.7 Hermitian Matrices and Hermitian Forms 166
4.7.1 Hermitian Matrices 167
4.7.2 Hermitian Forms 168
4.8 Positive Definite Hermitian Forms 169
4.9 Canonical Forms of a Hermitian Matrix Pair 173
4.10 Rayleigh Quotient 179
4.11 Problems and Exercises 183
Chapter 5 Decomposition of Linear Transformations and Matrices 186
5.1 Spectral Decomposition for Simple Linear Transformations and Matrices 186
5.1.1 Spectral Decomposition of Simple Transformations 186
5.1.2 Spectral Decomposition of Normal Transformations 194
5.2 Singular Value Decomposition for Linear Transformations and Matrices 201
5.3 Full Rank Factorization of Linear Transformations and Matrices 204
5.4 UR and QR Factorizations of Matrices 208
5.5 Polar Factorization ofLinear Transformations and Matrices 210
5.6 Problems and Exercises 214
Chapter 6 Norms for Vectors and Matrices 216
6.1 Norms for Vectors 216
6.2 Norms of Matrices 219
6.3 Induced Norns of Matrices 222
6.4 Sequences of Matrices and the Convergency 227
6.5 Power Series of Matrices 229
6.6 Problems and Exercises 231
Chapter 7 Functions of Matrices 233
7.1 Power Series Representation of a Function of Matrices 233
7.2 Jordan Representation of Functions of Matrices 235
7.3 Polynomial Representation of a Function of Matrices 237
7.4 The Lagrange-Sylvester Interpolation Formula 242
7.5 Exponential and Trigonometric Functions of Matrices 243
7.5.1 Complex Functions of Matrices 243
7.5.2 Real Functions of Matrices 246
7.6 Problems and Exercises 247
Chapter 8 Matrix-valued Functions and Applications to Differential Equations 248
8.1 Matrix-valued Functions 248
8.2 Derivative and Integration ofMatrix-valued Functions 250
8.3 Linear Dependency of Vector-valued Functions 252
8.4 Norms on the Space of Matrix-valued Functions 256
8.5 The Differential Equation ?(t)=A(t)X(t) 259
8.6 Solution to the State Equation ?(t)=Ax(t)+Bu(t) 263
8.7 Application of the Matrix Exponential Ⅰ:The Stability Theory 264
8.8 Application of the Matrix Exponential Ⅱ:Controllabilitv and Observability 266
8.8.1 Notion on Controllability 266
8.8.2 Tests for Controllabilitv 268
8.8.3 Observability and the Tests 271
8.8.4 Tests for Observability 272
8.8.5 Essentials ofControllability and Observability 274
8.8.6 State-Feedback and Stabilization 276
8.8.7 Observer Design and Output Injection 278
8.8.8 Co-prime Factorization of a Transfer Function Matrix over H∞ 280
8.8.9 Controllability and Observability Gramian 284
8.8.10 Balanced Realization 286
8.9 Application of the Matrix Exponential Ⅲ:The Hankel Operator 288
8.9.1 The Notion of a Hankel Operator 288
8.9.2 The Singular Values of a Hankel Operator 289
8.9.3 Schmidt Decomposition of a Hankel Operator 290
8.10 Notes and References 293
8.11 Problems and Exercises 293
Chapter 9 Generalized Inverses of Linear Transformations and Matrices 295
9.1 The Generalized Inverse of Linear Transformations and Matrices 295
9.1.1 The Generalized Inverse ofLinear Transformations 295
9.1.2 Generalized Inverses of Matrices 301
9.2 The Reflexive Generalized Inverse of Linear Transformations and Matrices 305
9.2.1 The Reflexive Generalized Inverse of Linear Transformations 305
9.2.2 The Reflexive Generalized Inverse of Matrices 308
9.3 The Pseudo Inverse ofLinear Transformations and Matrices 309
9.4 Generalized Inverse and Applications to Linear Equations 314
9.4.1 Consistent Inhomogeneous Linear Equation 314
9.4.2 Minimum Norm Solution to a Consistent Inhomogeneous Linear Equation 315
9.5 Best Approximation to an Inconsistent Inhomogeneous Linear Equation 317
9.6 Notes and References 319
9.7 Problems and Exercises 319
Chapter 10 Solution to Matrix Equations 320
10.1 The Notion of Kronecker Product and the Properties 320
10.2 Eigenvalues and Eigenvectors of Kronecker Product 324
10.3 Column and Row Expansions of Matrices 326
10.4 Solution to Linear Matrix Equations 327
10.5 Solution to Continuous-time Algebraic Riccati Equations 330
10.6 Solution to Discrete-time Algebraic Riccati Equations 336
10.7 Discussions and Problems 340
Bibliography 343
Notation and Symbols 346
List of Acronyms 348
- 《线性代数简明教程》刘国庆,赵剑,石玮编著 2019
- 《高含硫气藏开发腐蚀控制技术与实践》唐永帆,张强 2018
- 《钢铁行业污染特征与全过程控制技术研究》周长波等 2019
- 《高等代数 下》曹重光,生玉秋,远继霞 2019
- 《线性代数及应用》蒋诗泉,叶飞,钟志水 2019
- 《极线杀手 来自严寒》(西)维克托·桑托斯 2019
- 《生活垃圾焚烧飞灰中典型污染物控制技术》朱芬芬等编著 2019
- 《线性代数》孟红玲主编 2017
- 《钢铁烧结烟气多污染物过程控制原理与新技术》甘敏,范晓慧著 2019
- 《大学数学名师辅导系列 大学数学线性代数辅导》李永乐 2018
- 《市政工程基础》杨岚编著 2009
- 《家畜百宝 猪、牛、羊、鸡的综合利用》山西省商业厅组织技术处编著 1959
- 《《道德经》200句》崇贤书院编著 2018
- 《高级英语阅读与听说教程》刘秀梅编著 2019
- 《计算机网络与通信基础》谢雨飞,田启川编著 2019
- 《看图自学吉他弹唱教程》陈飞编著 2019
- 《法语词汇认知联想记忆法》刘莲编著 2020
- 《培智学校义务教育实验教科书教师教学用书 生活适应 二年级 上》人民教育出版社,课程教材研究所,特殊教育课程教材研究中心编著 2019
- 《国家社科基金项目申报规范 技巧与案例 第3版 2020》文传浩,夏宇编著 2019
- 《流体力学》张扬军,彭杰,诸葛伟林编著 2019
- 《指向核心素养 北京十一学校名师教学设计 英语 七年级 上 配人教版》周志英总主编 2019
- 《北京生态环境保护》《北京环境保护丛书》编委会编著 2018
- 《指向核心素养 北京十一学校名师教学设计 英语 九年级 上 配人教版》周志英总主编 2019
- 《抗战三部曲 国防诗歌集》蒲风著 1937
- 《高等院校旅游专业系列教材 旅游企业岗位培训系列教材 新编北京导游英语》杨昆,鄢莉,谭明华 2019
- 《中国十大出版家》王震,贺越明著 1991
- 《近代民营出版机构的英语函授教育 以“商务、中华、开明”函授学校为个案 1915年-1946年版》丁伟 2017
- 《新工业时代 世界级工业家张毓强和他的“新石头记”》秦朔 2019
- 《智能制造高技能人才培养规划丛书 ABB工业机器人虚拟仿真教程》(中国)工控帮教研组 2019
- 《陶瓷工业节能减排技术丛书 陶瓷工业节能减排与污染综合治理》罗民华著 2017