# Lie Groups and Algebras: Matrix Approach

Chapter

## Abstract

The Lie algebra g of a Lie group G is by definition the tangent space to G (considered as an analytic manifold) at the identity. When G is a matrix Lie algebra the elements of g may be obtained by differentiating curves of matrices. For example, the curve in has as its tangent vector at the identity \( \delta R = \dot R(0) = (_1^0{}_0^{ - 1}) \).

*SO*(2) given by$$ R(\theta ) = (_{\sin \theta }^{\cos \theta }{}_{\cos \theta }^{ - \sin \theta }) $$

## Keywords

Tangent Vector Parameter Group Matrix Approach Infinitesimal Generator Jordan Canonical Form
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1986