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

The general linear group of degree \(n\) is the set \(n\times n\) invertible matrices , together with matrix multiplication. Depending on the overlying field it is denoted by \(\GL(n,\mathbb{R})\) or \(\GL(n, \mathbb{C})\).

Remarks

\((\GL(n, \mathbb{R}), \cdot )\) and \((\GL(n, \mathbb{C}), \cdot)\) are topological groups
\(\GL(n)\) acts on \(\mathbb{R}^n\).

Subgroups Link to heading

orthogonal group