Let $n\in\mathbb N$. Every subgroup $H\le GL(n,\mathbb C)$ that is closed in the [subspace topology](/page/Subspace%20Topology) inherited from $M(n,\mathbb C)$ is a matrix Lie group, regarded as a real Lie group embedded in $GL(n,\mathbb C)$. Likewise, every subgroup $K\le GL(n,\mathbb R)$ that is closed in the subspace topology inherited from $M(n,\mathbb R)$ is a real matrix Lie group embedded in $GL(n,\mathbb R)$.