General Linear Group

In mathematics, the general linear group of degree $n$ is the set of $n\times n$ invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the group.

The group is so named because the columns (and also the rows) of an invertible matrix are linearly independent, hence the vectors/points they define are in General Linear Position, and matrices in the general linear group take points in general linear position to points in general linear position.

The notation ${\mathrm{GL}}_n(F)$ is a general linear group of degree $n$ over Field $F$