图书介绍

矩阵群 李群理论基础 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

矩阵群 李群理论基础 英文
  • AndrewBaker编著 著
  • 出版社： 北京：清华大学出版社
  • ISBN：9787302214847
  • 出版时间：2009
  • 标注页数：330页
  • 文件大小：8MB
  • 文件页数：346页
  • 主题词：李群－高等学校－教材－英文

PDF下载


点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快]温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页直链下载[便捷但速度慢]  [在线试读本书]   [在线获取解压码]
点击复制MD5值：8a239600afacf802569b05d7dbde2dc4

下载说明

矩阵群 李群理论基础 英文PDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

点击复制85GB完整离线版磁力链接到迅雷FDM等BT下载工具进行下载  详情点击-查看共享计划
建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

图书目录

Part Ⅰ．Basic Ideas and Examples3

1．Real and Complex Matrix Groups3

1.1 Groups of Matrices3

1.2 Groups of Matrices as Metric Spaces5

1.3 Compactness12

1.4 Matrix Groups15

1.5 Some Important Examples18

1.6 Complex Matrices as Real Matrices29

1.7 Continuous Homomorphisms of Matrix Groups31

1.8 Matrix Groups for Normed Vector Spaces33

1.9 Continuous Group Actions37

2．Exponentials, Differential Equations and One-parameter Sub-groups45

2.1 The Matrix Exponential and Logarithm45

2.2 Calculating Exponentials and Jordan Form51

2.3 Differential Equations in Matrices55

2.4 One-parameter Subgroups in Matrix Groups56

2.5 One-parameter Subgroups and Differential Equations59

3．Tangent Spaces and Lie Algebras67

3.1 Lie Algebras67

3.2 Curves,Tangent Spaces and Lie Algebras71

3.3 The Lie Algebras of Some Matrix Groups76

3.4 Some Observations on the Exponential Function of a Matrix Group84

3.5 SO(3) and SU(2)86

3.6 The Complexification of a Real Lie Algebra92

4．Algebras,Quaternions and Quaternionic Symplectic Groups99

4.1 Algebras99

4.2 Real and Complex Normed Algebras111

4.3 Linear Algebra over a Division Algebra113

4.4 The Quaternions116

4.5 Quaternionic Matrix Groups120

4.6 Automorphism Groups of Algebras122

5．Clifford Algebras and Spinor Groups129

5.1 Real Clifford Algebras130

5.2 Clifford Groups139

5.3 Pinor and Spinor Groups143

5.4 The Centres of Spinor Groups151

5.5 Finite Subgroups of Spinor Groups152

6．Lorentz Groups157

6.1 Lorentz Groups157

6.2 A Principal Axis Theorem for Lorentz Groups165

6.3 SL2(C) and the Lorentz Group Lor(3,1)171

Part Ⅱ．Matrix Groups as Lie Groups181

7．Lie Groups181

7.1 Smooth Manifolds181

7.2 Tangent Spaces and Derivatives183

7.3 Lie Groups187

7.4 Some Examples of Lie Groups189

7.5 Some Useful Formulae in Matrix Groups193

7.6 Matrix Groups are Lie Groups199

7.7 Not All Lie Groups are Matrix Groups203

8．Homogeneous Spaces211

8.1 Homogeneous Spaces as Manifolds211

8.2 Homogeneous Spaces as Orbits215

8.3 Projective Spaces217

8.4 Grassmannians222

8.5 The Gram-Schmidt Process224

8.6 Reduced Echelon Form226

8.7 Real Inner Products227

8.8 Symplectic Forms229

9．Connectivity of Matrix Groups235

9.1 Connectivity of Manifolds235

9.2 Examples of Path Connected Matrix Groups238

9.3 The Path Components of a Lie Group241

9.4 Another Connectivity Result244

Part Ⅲ．Compact Connected Lie Groups and their Classification244

10．Maximal Tori in Compact Connected Lie Groups251

10.1 Tori251

10.2 Maximal Tori in Compact Lie Groups255

10.3 The Normaliser and Weyl Group of a Maximal Torus259

10.4 The Centre of a Compact Connected Lie Group263

11．Semi-simple Factorisation267

11.1 An Invariant Inner Product267

11.2 The Centre and its Lie Algebra270

11.3 Lie Ideals and the Adjoint Action272

11.4 Semi-simple Decompositions276

11.5 Structure of the Adjoint Representation278

12．Roots Systems,Weyl Groups and Dynkin Diagrams289

12.1 Inner Products and Duality289

12.2 Roots systems and their Weyl groups291

12.3 Some Examples of Root Systems293

12.4 The Dynkin Diagram of a Root System297

12.5 Irreducible Dynkin Diagrams298

12.6 From Root Systems to Lie Algebras299

Hints and Solutions to Selected Exercises303

Bibliography323

Index325

热门推荐