- Title Pages
- Preface
- 1 Smooth manifolds
- 2 Matrices and Lie groups
- 3 Introduction to vector bundles
- 4 Algebra of vector bundles
- 5 Maps and vector bundles
- 6 Vector bundles with ℂ<sup>n</sup> as fiber
- 7 Metrics on vector bundles
- 8 Geodesics
- 9 Properties of geodesics
- 10 Principal bundles
- 11 Covariant derivatives and connections
- 12 Covariant derivatives, connections and curvature
- 13 Flat connections and holonomy
- 14 Curvature polynomials and characteristic classes
- 15 Covariant derivatives and metrics
- 16 The Riemann curvature tensor
- 17 Complex manifolds
- 18 Holomorphic submanifolds, holomorphic sections and curvature
- 19 The Hodge star
- List of lemmas, propositions, corollaries and theorems
- List of symbols
- Index

# Matrices and Lie groups

# Matrices and Lie groups

- Chapter:
- (p.14) 2 Matrices and Lie groups
- Source:
- Differential Geometry
- Author(s):
### Clifford Henry Taubes

- Publisher:
- Oxford University Press

This chapter discusses the following: the general linear group; Lie groups; examples of Lie groups; some complex Lie groups; the three most commonly seen subgroups of Gl(n; ℂ): Sl(n; ℂ), U(n) and SU(n); and notation with regards to matrices and differentials.

*Keywords:*
matrices, linear algebra, linear group, Lie groups, differentials

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- Title Pages
- Preface
- 1 Smooth manifolds
- 2 Matrices and Lie groups
- 3 Introduction to vector bundles
- 4 Algebra of vector bundles
- 5 Maps and vector bundles
- 6 Vector bundles with ℂ<sup>n</sup> as fiber
- 7 Metrics on vector bundles
- 8 Geodesics
- 9 Properties of geodesics
- 10 Principal bundles
- 11 Covariant derivatives and connections
- 12 Covariant derivatives, connections and curvature
- 13 Flat connections and holonomy
- 14 Curvature polynomials and characteristic classes
- 15 Covariant derivatives and metrics
- 16 The Riemann curvature tensor
- 17 Complex manifolds
- 18 Holomorphic submanifolds, holomorphic sections and curvature
- 19 The Hodge star
- List of lemmas, propositions, corollaries and theorems
- List of symbols
- Index