\(
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\require{physics}
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\)
Math and science::Algebra::Aluffi
Subgroups of the general linear group
Below are three subgroups of \( \mathrm{GL}_n(\mathbb{R})\), the group of invertible
\( n\times n\) matrices with real entries.
- \( \mathrm{SL}_n(\mathbb{R})\)
- The subset of \( \mathrm{GL}_n(\mathbb{R})\) consisting of [what matricies?]. "S" is short for "special".
- \( \mathrm{O}_n(\mathbb{R})\)
- The subset of \( \mathrm{GL}_n(\mathbb{R})\) consisting of
[what matricies?].
"O" here is short for "orthogonal".
- \( \mathrm{SO}_n(\mathbb{R})\)
- The subset of \( \mathrm{O}_n(\mathbb{R})\) consisting of
[what matricies?].
Can you proof that these 3 subsets form subgroups?
