(group theory) For given field F and order n, the group of invertible n×n matrices, with the group operation of matrix multiplication.

(group theory) For given field F and order n, the group of n×n matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion.

(algebraic geometry, category theory) An algebraic group that is isomorphic to a subgroup of some general linear group.

In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P(V).