Let \(n\geq 1\). The orthogonal group is \[ \Orth_n(\CC) \coloneqq \theset{ A\in\Mat_{n\times n}(\CC) \st A^tA = AA^t = I }. \]
\(\Orth_n(\CC)\) is a complex Lie group of dimension \(n(n-1)/2\).
Orthogonal group $\Orth_n(\CC)$
D-3ZPR7
D-3ZPR7
Let \(n\geq 1\). The orthogonal group is \[ \Orth_n(\CC) \coloneqq \theset{ A\in\Mat_{n\times n}(\CC) \st A^tA = AA^t = I }. \]
\(\Orth_n(\CC)\) is a complex Lie group of dimension \(n(n-1)/2\).