Definition:General Linear Group

Definition
The general linear group over a field $$F \ $$, denoted $$\text{GL}_n(F) \ $$ is defined as the group of all $$n\times n \ $$ matrices with elements over $$F \ $$ with non-zero determinant.

Subgroups of the General Linear Group
Definition:Special Linear Group

Definition:Unitary Group

Definition:Orthogonal Group

Definition:Symplectic Group

Definition:Triangular Matrix Groups

Related Groups
Definition:Projective Linear Group

Definition:Affine Group

Definition:General Semilinear Group

Definition:Infinite General Linear Group