\[ \DeclareMathOperator{\O}{O} \DeclareMathOperator{\GL}{GL} \]

The orthogonal group \(\O(n)\) acts continuously on \(\mathbb{R}^n\) via vector-matrix multiplication.

See also Link to heading

• action of \(\GL(n)\) on \(\mathbb{R}^n\)
• action of \(\O(n)\) on \(\mathbb{S}^{n-1}\)