Set of invertible matrices with real entries

  • #1
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##GL(n,\mathbb{R})## is set of invertible matrices with real entries. We know that
[tex]SO(n,\mathbb{R}) \subset O(n,\mathbb{R}) \subset GL(n,\mathbb{R})[/tex]
is there any specific subgroups of ##GL(n,\mathbb{R})## that is highly important.
 
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Answers and Replies

  • #2
jgens
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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.
 
  • #3
George Jones
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Other important subgroups are the pseudo-orthogonal groups O(p,g) and SO(p,q) (e.g., the Lorentz group) and the symplectic groups.
 
  • #4
jgens
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There is an embedding GL(n,C) < GL(2n,R) so all the important subgroups of GL(n,C) like the unitary groups can be regarded as subgroups of GL(2n,R) as well.
 

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