Some of the things I've learned every day since Oct 10, 2016
81: General Linear Groups
January 1, 2017Posted by on
The general linear group , where is a vector space, is the group of all automorphisms under the operation of composition of linear transformations.
When is over the field and is finite-dimensional with , this group is isomorphic to the group of invertible matrices with entries from under the operation of matrix multiplication. In this case, the group is often written as .
General linear groups are used in group representations. A group representation is a representation of a group as a general linear group. That is, it is an automorphism
where is the group being represented and is any vector space.