# Set of invertible matrices with real entries

##GL(n,\mathbb{R})## is set of invertible matrices with real entries. We know that
$$SO(n,\mathbb{R}) \subset O(n,\mathbb{R}) \subset GL(n,\mathbb{R})$$
is there any specific subgroups of ##GL(n,\mathbb{R})## that is highly important.

Last edited:

jgens
Gold Member
You named most of the big ones. I would definitely add SL(n,R) to that list. Some of the subgroups consisting of diagonal matrices and say upper triangular matrices are important too.

George Jones
Staff Emeritus