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

The general linear group \(\GL(n)\) acts continuously on \(\mathbb{R}^n\) (or \(\mathbb{C}^n\)) via vector-matrix multiplication.

See also Link to heading

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