# Math Help - When is GL(V) finite?

1. ## When is GL(V) finite?

If V has finite dimension does this imply that GL(V) is finite?

2. Originally Posted by Smancer
If V has finite dimension does this imply that GL(V) is finite?
If $V$ is a finite dimensional vector space over the field $F$ say of degree $n$. Then there is an vector space isomorphism $\theta : V\to F^n$. Therefore, $\text{GL}(V)$ is isomorphic to $\text{GL}(n,F)$ which is a finite group.