Matrix Lie group

Summary

A matrix Lie group is a closed subgroup of the general linear group $GL_n(\C)$. By the closed subgroup theorem, every matrix Lie group is a Lie group, and its Lie algebra can be computed with the matrix exponential. Most Lie groups met in practice, such as the orthogonal, unitary and symplectic groups, are matrix Lie groups. So they are a common entry point to Lie theory.