Category:Definitions/General Linear Group

This category contains definitions related to General Linear Group.
Related results can be found in Category:General Linear Group.

Let $K$ be a field.

The set of all nonsingular order-$n$ square matrices over $K$ is a group under (conventional) matrix multiplication.

This group is called the general linear group (of degree $n$) and is denoted $\GL {n, K}$, or $\GL n$ if the field is implicit.

The field itself is usually $\R$, $\Q$ or $\C$, but can be any field.