Ciro Santilli $$ Sponsor Ciro $$ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱

Orthogonal group ( $O (n)$ )

| nosplit | ↑ parent "Important Lie group" | words: 0 | descendant words: 1k | descendants: 22

nosplit | ⇓ toc | ↑ parent "Important Lie group" | Wikipedia | words: 0 | descendant words: 1k | descendants: 22

Tags: Isometry group

Table of contents | 0, 1k, 22
- Definition of the orthogonal group | 8, 391, 4 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
- Topology of the orthogonal group | 0, 343, 2 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
  - The orthogonal group is compact | 🔗 link | nosplit | ↑ parent "Topology of the orthogonal group"
  - Connected components of the orthogonal group (The orthogonal group has two connected components) | 343 | 🔗 link | nosplit | ↑ parent "Topology of the orthogonal group"
- Lie algebra of $O (n)$ | 9 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
- Special orthogonal group ( $S O (n)$ , Rotation group) | 46, 275, 3 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
  - Lie algebra of $S O (3)$ | 180, 211, 1 | 🔗 link | nosplit | ↑ parent "Special orthogonal group"
    - Lie bracket of the rotation group | 31 | 🔗 link | nosplit | ↑ parent "Lie algebra of $S O (3)$ "
  - 3D rotation group ( $S O (3)$ ) | 18 | 🔗 link | nosplit | ↑ parent "Special orthogonal group"
- Unitary group ( $U (n)$ ) | 80, 205, 8 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
  - Unitary group of degree 1 ( $U (1)$ ) | 🔗 link | nosplit | ↑ parent "Unitary group"
  - Unitary group of degree 2 ( $U (2)$ ) | 5 | 🔗 link | nosplit | ↑ parent "Unitary group"
  - Unit circle | 19 | 🔗 link | nosplit | ↑ parent "Unitary group"
  - Special unitary group ( $S U (n)$ ) | 49, 101, 4 | 🔗 link | nosplit | ↑ parent "Unitary group"
    - Special unitary of degree 2 ( $S U (2)$ ) | 34, 52, 3 | 🔗 link | nosplit | ↑ parent "Special unitary group"
      - Representations of $S U (2)$ | 0, 18, 2 | 🔗 link | nosplit | ↑ parent "Special unitary of degree 2"
        
        Lie algebra of $S U (2)$ | 10 | 🔗 link | nosplit | ↑ parent "Representations of $S U (2)$ "
        
        2D representation of $S U (2)$ | 8 | 🔗 link | nosplit | ↑ parent "Representations of $S U (2)$ "

Ancestors

Important Lie group | 0, 5k, 65
Lie group | 278, 7k, 97
Differential geometry | 12, 7k, 98
Geometry | 0, 9k, 154
Mathematics | 17, 34k, 763
Ciro Santilli's Homepage | 262, 237k, 4k

Incoming links

All indefinite orthogonal groups of matrices of equal metric signature are isomorphic | 179
Connected components of the orthogonal group | 343
Definition of the indefinite orthogonal group | 204, 383, 1
Finite special general linear group | 51
Indefinite orthogonal group | 38, 421, 3
Isometry group | 69, 206, 1
Orthogonal matrix | 11, 56, 1
Special orthogonal group | 46, 275, 3
Symplectic group | 222, 222, 2
Topology | 152, 2k, 61
Unitary group | 80, 205, 8