##  [General Linear Group](/general-linear-group) 

  ##  [General Linear Group](https://algebra.quantumdictionary.io/general-linear-group-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The group of all invertible n-by-n matrices over a specified field or ring, with the group operation given by matrix multiplication; members are exactly those matrices that admit a two-sided inverse of the same size over the chosen base.