Lie Groups

Overview

A Lie group {% G %} is a group which is also a manifold so that the map 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

Examples

• Rotation Group