The orthogonal group of degree \(n\) is the set \(n\times n\) orthogonal matrices , together with matrix multiplication. It is denoted by \(\O(n)\).
Remarks
- The orthogonal group \(\O(n)\) is a subgroup of the general linear group \(\GL(n,\mathbb{R})\).
- The orthogonal group \(\O(n)\) is the group of distance-preserving transformations of dimension \(n\).
- The orthogonal group is topological group.
- \(\O(n)\) acts on \(\mathbb{R}^n\)