Overview
A Lie group {% G %} is a group which is also a manifold so that the map
{% (g,h) \rightarrow g \dot h^{-1} %}
is smooth.
Matrix Lie Group Classifications
- General Linear Group GL(n) {% n \times n %} non-singular matrices
- Special Linear Group - subgroup of GL(n) with determinant 1
- Orthogonal Group - subgroup of GL(n) with Orthogonal rows and columns
- Special Orthogonal Group - subgroup of GL(n) that is both special and Orthogonal.
- Unitary Group - subgroup of GL(n) where the members are unitary, that is {% R^\dagger = R^{-1} %}
- Special Unitary Group