A linear group or matrix group is a group $G$ whose elements are invertible $n \times n$ matrices over a field $F$.
A matrix group is a group $G$ consisting of invertible matrices over a specified field $F$, with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group.
Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem.
As examples of linear groups, we have the general linear group, of all invertible $n\times n$ matrices, the special linear group, of all $n\times n$ matrices whose determinant is $1$, or the group of all invertible $n\times n$ upper triangular matrices.
