The orbits of the action of \(\GL(n)\) on \(\mathbb{R}^n\) are \(\mathbb{R}^n\setminus \{0\}\) and \(\{0\}\).
\[
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\O}{O}
\]
The orbits of the action of \(\GL(n)\) on \(\mathbb{R}^n\) are \(\mathbb{R}^n\setminus \{0\}\) and \(\{0\}\).